Simply saying a "theory" can be falsified in a number of ways is insufficient. The TOE is completely dependent upon the concept that mutation causes genetic change (affirmed), that while the vast majority (99.999%) of mutations are deletorious yet a tiny number are positive or neutral (affirmed), and therefore given a really long period of time that a sequence of neutral or positive mutations will result in new genera, families, orders, kindoms, and so forth of different species (NOT AFFIRMED). This statement is NOT falsifiable because only be observing over tens if not hundreds of thousands of years can it be affirmed. And only if it is not affirmed over that same long time period can it be falsified. This, and no other, is the key point.
And further, this concept (mutation causing a sequence of gradual changes, i.e. microevolution) is either sketchy, or not observed (depending on who is asked) in the fossil record, and I quote: "Reexamination of the fossil record led Steve Gould and Niles Eldridge to recognize that only a few examples of speciation by gradual change existed. In contrast, the fossil record documents long intervals of time during which species undergo little or no morphological change. These intervals are punctated by the sudden appearance of new species (and higher-order taxa) as a peripheral isolate.". Check out the site, it is no creationist mumbo jumbo site but rather a science page regarding plant evolution from Colby University in Maine. It is also the case that grouping the fossil record into a "tree" has come under attack from various directions. See What do terms like phylum, order and family mean?
So what say you? Classification into a "tree" or set of "trees" is under attack not by Creationists but by biologists, microevolution is only sketchy at best in the fossil record, and there is no way to refute the "give us a few tens of thousands of years and you'll see your evolution" argument (upon which the TOE hangs) -- and I say again that the TOE is no more falsifiable than astrology. And note you -- I am making no Creationist claims in my assertions!
And Gould is right. We forget that organisms are very well designed. Take the example of the bat. It is a mammal so its descent according to evolution is from mammals. However, its way of life, of feeding requires flight and excellent sonar. How could it live without one or the other? Answer is it could not, not for a single generation and we know that the huge number of mutations necessary to accomplish both would have taken millions of years - as Neo Darwinists will admit. But that is not the end of the problem. For flight you need muscles, for flight you need wings, and for flight you need very light bones - none of these features is found in other mammals. Therefore the bat could not have arisen by chance since so many of the features we see in it were necessary for it to survive even for one generation if they were not developed all at the same time.