The short answer

Yes, but the conditions under which this kind of error arises are well-understood, and cast no doubt on the general reliability of the method.

The longer answer

I. Such errors arise from misapplication or anomalous but well-understood conditions

As pointed out by zoologist Tim Berra (1990:38), many of the “obviously wrong dates” creationists point to come from misapplication of carbon dating to samples for which it was never supposed to work in the first place. The short half-life (5,730 years) of 14C (carbon-14) makes carbon dating accurate only up to 50,000 years, so in some cases creationists derive incorrect results by applying the test to samples older than 50,000 years. In other cases, such as that of the “3,000 year-old” mollusk, the error arises because of well-understood peculiarities in the environment from which the sample was derived. The mollusk incident is explained in full detail by Keith and Anderson (1963), and has no impact on the general reliability of carbon dating.

II. The maximum error range still does not allow for a young earth

The maximum error in proper 14C dating is only a few thousand years. This means that even with the worst kind of error on samples in the older range, the results of 14C dating leave no room for the 6,000 to 10,000 year-old earth desired by young-earth creationists.

References

Berra TM. 1990. Evolution and the Myth of Creation. Oxford: Oxford University Press.

Keith MS and Anderson GM. 1963. Radiocarbon dating: fictitious results with mollusk shells. Science 141:634.