LOL! Look, we're not talking about million year old monkey bones here. C-14 dating is generally reliable for anything less than 50,000 years old. I say "generally" because it does vary slightly based on surrounding environmental conditions, and older samples can be off by a couple thousand years (a whisker by the timescales we're discussing). Still, sometimes flukes do happen, which is why generalized statements like "the humans wiped out the sloths" have to be backed up by numerous datings from geographically diverse sites.
In this case, the fossil record is heavy enough to corroborate this theory and offer useful averages. We can tell, for instance, that North America wasn't widely populated by humans 50,000 years ago because the bones dug up so far are almost exclusively newer than that (yes, I know about the flukes, but those could be misreads or even examples of very early explorers). We also know that sloth bones used to be common. We know that the C-14 shows that human remains start showing up around point X, and that sloth remains stop showing up shortly afterward.
It's really not important whether Date X happened 20,000 years ago or 15,000 years ago, but simply that the dating techniques show that the two sets of events happened at the same time.
We're dealing with the last 50,000 years, so most of the dating is probably Carbon-14 dating.
Where do you see the inaccuracies in this method? It seems to work fine for me.
Please post peer-reviewed scientific challenges to modern dating methods.
Although they are still used as a bit rough, they are pretty accurate in terms of magnitude.