What would a CRC64 do better than, say, using the first 64 bits of the SHA-256 (other than performance, of course)? I see talk of CRCs always catching contiguous errors smaller than the CRC size, is it just that a CRC is guaranteed to do that and a 64-bit cryptographic hash isn't?
Yes. CRC is linear in the data and the error. This makes it easy to analyze the crc of specific error sets, and if non of them have zero crc, then if the error is in that set it is guaranteed to be found.
