I just want to add a personal observation regarding the nickel.
While they don't show a close-up of it in the episode where they find it, they did on the "aftershow",
here.
For comparison,
here is a shot of a 1964 nickel in the condition as-minted back in 1964.
Notice how much wear there is around the brow and cheek, the highest points on the surface. The claim is that this coin was dropped in a hole in 1964. So, a best estimate is that it had seen about 6 months of circulation wear, but a year at most. This is subjective, I don't have a study to cite, but they just don't wear down that quickly unless there were some extreme circumstances. And being in the ground alone won't do it... it may very well discolor it, especially if it's in highly mineralized soil. But it won't wear the high points down like that.
I highly doubt this coin has been in the earth since 1964. As Erik said himself, it could've just been exposed in the spoils pit... it's not as if people don't simply drop/lose coins now and then, and this could have been dropped anytime since 1964, and was sitting near the surface until they dug their pit and it fell in. The same is true for the chips of ceramic, which appear to be nothing special. It would certainly explain why they said they drilled for 40 feet and only saw a few small chips... because they had nothing to do with the interior of the mesa.
Beyond that, they apparently claim the nickel also came from "deep within the mesa", which is solid rock. Who does archeological "digs" into solid rock, and how could they ever backfill that if they tried?