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I do not think you are willing to listen to anything which might disturb your beliefs. However, you have challenged Carbon-14 dating, which I use and trust, so for the benefit of others on this thread I will respond.

Note: I am including your comments in italics and my responses in blockquotes (indented). Also, most of my responses are my own, and any other sources I use are cited.

I am aware that your post consists largely of The Problem of Carbon by William Tripp posted at http://www.drdino.com/articles.php?spec=79.

Radiocarbon dating, especially using the Carbon 14 method, takes advantage of the radioactive decay of the isotope, which is seen as a constant. Every living thing takes in and expels Carbon 14 while it is alive, and a static level of the element is maintained. When the organism dies, the infusion is suspended, and the level is reduced according to the rate of decay, known as the “half-life.” The amount of Carbon 14 in the artifact is measured and then compared to the presumed static level the organism maintained while alive; the comparison then yields the relative age of the specimen. Though this sounds very straightforward and scientific, there are several serious problems.

The first problem is seen in the very approach in the presumption that must be made in the level of Carbon 14 the organism had while living. Here we have a critical calculation that is based upon an assumption that an organism which lived thousands of years previous, of which there are no modern species to compare, developed a specific level of Carbon 14 from an environment we know nothing about. If for example, the presumption is inaccurate by only 10%, considering that it is the rate of decay that forms the mathematical constant, the inaccuracy of the calculation of age at the upper limit would be tens of thousands of years.

This last paragraph heads off the deep end. We do know about the level of Carbon-14 in past environments. Or rather, we can calibrate the radiocarbon curve based on a variety of things, including Bristlecone pines.
Weins says it better than I can: "For example growth rings in trees, if counted carefully, are a reliable way to determine the age of a tree. Each growth ring only collects carbon from the air and nutrients during the year it is made. To calibrate carbon-14, one can analyze carbon from the center several rings of a tree, and then count the rings inward from the living portion to determine the actual age. This has been done for the "Methuselah of trees", the bristlecone pine trees, which grow very slowly and live up to 6,000 years. Scientists have extended this calibration even further. These trees grow in a very dry region near the California-Nevada border. Dead trees in this dry climate take many thousands of years to decay. Growth ring patterns based on wet and dry years can be correlated between living and long dead trees, extending the continuous ring count back to 11,800 years ago." http://www.asa3.org/ASA/resources/Wiens.html#page%2012
One more comment, if the "presumption is inaccurate by only 10%" then the resulting date will be inaccurate by 10%, not "tens of thousands of years" as the radiocarbon method only goes back some 50,000 years. So the most you could have with a 10% error is 5,000 years. If fact, most radiocarbon dates used by archaeologists are in the 12,000 or less range, so the error in this example would be 1,200 years at the most. With the calibration curve that has been worked out for the past 12,000 years I doubt there is anywhere near such an error. (I am not sure why you are so worried about potential errors in the Carbon-14 method, as scientists use other methods to date fossils anyway.)

The very basis for the assumption above is another problem, and is perhaps the most embarrassing for the proponents of radiocarbon dating. To assume a particular level of Carbon 14 in an organism requires a precise determination of environmental (atmospheric) levels of the same. That is, to presume a particular level in a living thing requires a precise knowledge of the ambient amount of Carbon 14 in the air and environment. Scientists performing radiocarbon dating assume that the amount in the environment has not changed. This is compelling for several reasons, not the least of which is the convenience with which “science” apparently operates; we hear of massive changes in the earth, ice ages, catastrophic events that killed the dinosaurs, etc., but the environment never changed according to the same scientists.

Actually scientists assume that changes did occur in the amount of Carbon-14 in the atmosphere and the environment. That is why so much effort has been put into the calibration curve.

Not only does the requisite level of assumption and presumption all but invalidate the accuracy of the claims of very old dating, but were there for example, an environmental phenomenon that affected the level of ambient Carbon 14, the results could be skewed exponentially. In fact, several such phenomena did indeed exist, proven by the same science that supports old-age radiocarbon dating! It would seem quite clear that some predisposition or predilection for particular findings in terms of dating artifacts is at work in this case. For example, consider that it is essentially accepted that an antediluvian water canopy existed surrounding the earth; this would have acted to either negate or at least significantly reduce the effect of cosmic, x-ray, and ultraviolet radiation in the upper atmosphere. Carbon 14 production would have been negligible, and therefore would not have been absorbed by living things; any organism living before the reduction of the canopy would in turn be dated exponentially older than it actually is. Or consider the effect a global atmospheric shield of dust created as a result of a meteor impact some scientists believe killed off the dinosaurs—levels of Carbon 14 in the atmosphere must certainly have been different, thereby invalidating the age/date test data. Isn’t it funny how the same scientists who purport constant catastrophic changes in earth’s history depend upon the inherent necessity that it was completely without any changes?

This paragraph is full of errors. First Carbon-14 is not used for "very old dating." Second, there is no scientific evidence that "an antediluvian water canopy existed surrounding the earth." And even if there was it would not change the production of Carbon-14 in the outer atmosphere. Third, "a global atmospheric shield of dust created as a result of a meteor impact some scientists believe killed off the dinosaurs" was some 60+ million years ago, while the Carbon-14 method we are dealing with is limited to 50,000 years. And the dust probably would not change anything anyway, as it would not have been in the outer atmosphere! (If only you could think as critically about the "antediluvian water canopy" as you pretend to do about Carbon-14 dating.)

Moreover, it is established fact that the earth’s magnetic field has been in a constant decline in strength2, which would have vigorously protected the earth from the same radiation, all but negating the production of Carbon 14 and thereby minimizing the ambient amount available for absorption by living things. Yet these two facts are virtually unknown in modern society, and it seems never associated with radiometric dating, apparently since it would put such method (and indeed its findings) in doubt as to its reliability.

We are talking about the last 50,000 years, during which Carbon-14 dating is applied. There is no evidence the earth’s magnetic field has changed much in this time period.

Another fact, which proves quite embarrassing to “old-age” proponents in regard to radiometric dating, is the half-life of Carbon 14 itself. Not only is the actual half-life length itself in some contention, but the effect it would have on the upper limits of its capability in dating illustrates clearly the level of fraud that has been foisted on an unsuspecting society. Consider that Carbon 14’s half-life is around 5,630 years 3 (though estimates range from 5,300 to 5,700 years); in only ten cycles of this, there would be nothing left to measure in the extant specimen! This means that the absolute maximum age radiocarbon could date a specimen to would be around 56,300 years; yet daily society is barraged with reports that some new find was dated in the hundreds of thousands, and even millions of years using Carbon 14. Actually, after the sixth cycle or so, there would not be enough Carbon 14 in the sample to be measured; the upper limit then would be around 30,000 years.

The half life of Carbon-14 is not a problem, as it is rather closely established. It is also well known to everyone but creationists that the Carbon-14 method cannot be used beyond about 50,000 years. Certainly dates in excess of 30,000 years have to be taken as estimates. So?

This leads to yet another inherent problem in the use of radiometric dating which would seem virtually insurmountable, and is caused by the presence of environmental Carbon 14 itself, ironically, the phenomenon scientists exploit in the determination of date of origin. Simply stated, it is nearly impossible to preclude contamination that seriously affects the results of the measurement. The levels of Carbon 14 in any “old” artifact are extremely low; because of this, it is virtually impossible to prevent the test and measurement equipment from picking up residual or background environmental Carbon 14 not associated with the specimen.

Contamination is a real problem! That is absolutely right. Especially at the oldest end of the range. That's why archaeologists don't smoke during sample collection, and laboratories go to great lengths to ensure samples are clean. And that is why a dinosaur bone can have some residual Carbon-14 (but the CS types make lots of hay from that one; google something like "dating dinosaur bones" for a good laugh.)

Further, most artifacts by their very nature are found in and around various forms of rock, which provide several sources of additional radiation. This has the concomitant effect of providing a source of neutrino radiation; Carbon 14 decay is accelerated in the presence of such bombardment, and again the effect would be to cause the specimen to appear much older than it actually is. This effect cannot be overstated in regard to the estimates of age—a less than 5% reduction in the extant amount of Carbon 14 in the specimen, owing to the “constant” of its half-life will yield a factor of 5 times the actual age. Imagine the effect on science if an artifact dated at 45,000 years is actually only 9,000; the possibilities are staggering.

Actually most artifacts are found in soil; as most early peoples lived in productive environments, soil was important either for early agriculture or for the plants and animals it supported. Caves were used, but not as much as one might think.
Also, many of the items dated by archaeologists are not artifacts. Charcoal from firepits is an ideal material. Bones and shells work well too. I particularly like marine shell, particularly mussel and abalone shells. They can be acid-etched to remove any possible contamination from the soil or fingerprints, etc.
"neutrino radiation"? Oh, horrors! We're all doomed! Not that kind of radiation? Oh, well. Neutrinos are produced by the sun and have very little interaction with the earth--they sail right through without even noticing it. It is very difficult to even catch one as they don't really want interact with much of anything. Oh, well. Another hypothesis spoiled by a nasty little fact (isn't science fun?).
Actually Weins has a good paragraph on this one: "Some people have tried to defend a young Earth position by saying that the half-lives of radionuclides can in fact be changed, and that this can be done by certain little-understood particles such as neutrinos, muons, or cosmic rays. This is stretching it. While certain particles can cause nuclear changes, they do not change the half-lives. The nuclear changes are well understood and are nearly always very minor in rocks. In fact the main nuclear changes in rocks are the very radioactive decays we are talking about." http://www.asa3.org/ASA/resources/Wiens.html#page%2023
"a less than 5% reduction in the extant amount of Carbon 14 in the specimen, owing to the “constant” of its half-life will yield a factor of 5 times the actual age." My math has never been too good, but wouldn't a 5% difference in the amount of Carbon-14 lead to a date that was 5% off?

The foregoing is [sic] but a few examples of the problems with Carbon 14; many more examples could be given, as well as some documented, glaring failures such as live clams being dated at 1,500 years, and parchment documents from the 17th century being dated to the 4th. The point however, is that radiocarbon dating has serious problems in terms of reliability and veracity, and its use is at best quite limited. On the other hand, there is an obvious dichotomy in these problems and the lack of common knowledge regarding them; it would seem that there should be some explanation why the vast majority of society is so unaware of the spurious nature of the science behind radiocarbon dating. That is, since science is ostensibly clinical and without emotion, the most likely cause of the dearth of knowledge of the limitations, fallacies, and vulnerabilities in this method is man himself—a manifestation of his own biases and predilections. This is the subject of the next division.

Several things of note here. First, you simply can't date live clams and get a reliable age. The nuclear tests beginning around World War II did what all the wishful thinking of the creationists can't do--messed up the intake of Carbon-14 in living creatures. Secondly, parchments are often treated with different chemicals, and that can contaminate dates. Finally, it has not been shown that "radiocarbon dating has serious problems in terms of reliability and veracity" or the "spurious nature of the science behind radiocarbon dating" or that "the most likely cause of the dearth of knowledge of the limitations, fallacies, and vulnerabilities in this method is man himself."
[Several paragraphs of opinion, ending with something about serpents and Eve, etc., has been omitted as irrelevant.]
You got yourself a looser here son. If you don't know anything about the Carbon-14 method it might be better if you stopped badmouthing it. Or at least seek out better websites for your quotemining.
If you have any specific questions let me know. If I can't answer them surely one of the others on these threads can.
But so far, science is ahead on this one by a knockout.

Reference:

Radiometric Dating: A Christian Perspective, by Dr. Roger C. Wiens. http://www.asa3.org/ASA/resources/Wiens.html