Not really. They find tiny levels of 14C in very old coals. All that means is that, in addition to the atmospheric source, there is a mechanism for producing very low levels of 14C within the earth - likely irradiation by exogenous radioactive sources.
As Baumgardner admits, even if you claimed a common age for all the coals, based on the 14C content, and said that was the age of the Genesis flood, you'd come up with an age of 50,000 years. So he then has to introduce the ad hoc assumption of 'accelerated nuclear decay', for which there is no plausible physical mechanism, to make it consistent with Genesis.
[snip]..."As for the contamination issue, someone asserted that any C14 date of 30,000 years or more is due to contamination. If this is so, then why do they say the method is accurate to 50,000 years? If any C14 date has ever yielded a value over 30,000 years, this implies that such contamination is not ubiquitous. Of course, it could be that older measurement techniques were less accurate. Now, 30,000 years is about 5 half lives of C14, which means that a contamination of 1/32 (slightly less) would be required to achieve this date for a sample of infinite age. This is a substantial contamination.
Anyway, as for C14 dating in general, it seems clear that many, many results are much too young according to the standard view, and that explaining away one or two of them does not appreciably diminish the problem.
Here is another instance of an anomalously young carbon 14 date:
At the 1992 Twin Cities Creation Conference, there was a paper presented called “Direct Dating of Cretaceous-Jurassic Fossils (and Other Evidences for Human-Dinosaur Coexistence)”. Among other things, the results of carbon-dating of Acrocanthosaurus bones are given.
The authors noted that dinosaur bones are frequently (“as a rule”) found with a black carbon residue of some sort on the bones. The authors speculated that this residue could be the leftovers of the decayed skin and flesh: they quote the Penguin Geology Encyclopedia’s definition of “carbonization”: “Carbonization; the reduction of organic tissue to a carbon residue. An unusual kind of fossilization in which the tissue is preserved as a carbon film. Plants are commonly preserved in this manner, soft-bodied animals more rarely.” Since this material is organic, it can be used to carbon-date the fossils.
The authors describe in detail the measures taken to ensure that no other source of carbon contamination was present inside or outside the bones. When the bones were ground up and carbon-dated, the dates they received from the lab from different methods were 9,890 to 36,500 years BP (before present)." source