corruption in disk blocks, network packets, etc.

checksum fixed-size, data any size

besides bit changes: swapping data (data order)

collisions

with checksums: drive hardware level 520 bytes per sector = 512 data + 8 checksum

overheads: disk space (negligible), memory space (negligible), 
 time (depends, do in parallel with copy, or in hardware),
 I/O (maybe extra)