I have worked at places where bad hardware has caused undetected errors in TCP file transmissions, because of the way that IP handles its checksums. IP checksums each packet as its transferred from machine to machine, and that checksum is recreated each hop. If something corrupts the packet data on a router, it may well stay corrupt and undetected on its way to the final destination.

(We ultimately found the problem because DECNet transfers did do end-to-end checksumming, and when transfers went through this particular router the DECNet stuff would fail but the IP stuff wouldn't. (It was just silently corrupted))

Moral of the story: If the data's truly important, do an end-to-end checksum of the files, just to be sure. You rarely need this sort of check, but if you're moving financial or medical data, you'd probably best do it to be extra sure.