You can use the fsck subcommand to check for problems in your data. What can be checked depends on the key-value backend you've used for the data. For example, when you use the SHA1 backend, fsck will verify that the checksums of your files are good. Fsck also checks that the annex.numcopies setting is satisfied for all files.

# git annex fsck
fsck some_file (checksum...) ok
fsck my_cool_big_file (checksum...) ok
...

You can also specify the files to check. This is particularly useful if you're using sha1 and don't want to spend a long time checksumming everything.

# git annex fsck my_cool_big_file
fsck my_cool_big_file (checksum...) ok