Every so often in my internet wanderings I run across a True Believer In Jesus throwing out Piltdown Man as a prime example of the unreliable nature of science; invariably it is presented as something scientists got horribly wrong and thus evolution is disproved, despite the fact that it was a deliberate, elaborate hoax that was always controversial and was uncovered and revealed to be a hoax by none other than scientists nearly 60 years ago, about the same time the structure of DNA was worked out by Watson and Crick.
No, it's not an example of what science does wrong; rather the contrary, I would think. By the time science got done with it, the thing was pretty well nailed to the wall. But it might be a good example to use for comparison with the way religious faith works. Here is a direct comparison of two major "archaeological finds" of the last 200 years.