You can't do a checksum on the remote files without downloading them
(unless there's some really funky FTP daemon that has a checksum SITE command, but haven't heard of one).
A guy I know worked on a custom ftp client years ago that would create checksum files for every file you uploaded, with a hash for each chunk of the file so you would only have to re-download corrupt pieces. Dunno if he ever produced even a proof-of-concept, I've never heard of other people doing this, and it would obviously only work for files that you've uploaded with the custom client. *shrug*.