Someone else mentioned further up that it's all zeroes or all ones. A checksum of all zeroes means "this packet has no checksum and that's okay". Because of the way it's calculated 0xffff works out the same as 0x0000, so if the checksum happens to sum to 0x0000 it's replaced with 0xffff.

Both values are totally valid checksums but some people don't believe that :-)

Usually all 0s or all Fs. I had the same problem with an old Dell PowerEdge with Broadcom nics... packet failures left and right without disabling the offloading options.