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 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

If you have a large repo, you may want to check it in smaller steps. You may start and continue an aborted or time-limited check.

# git annex fsck -S <optional-directory> --time-limit=1m
fsck some_file (checksum...) ok
fsck my_cool_big_file (checksum...) ok

  Time limit (1m) reached!

# git annex fsck -m <optional-directory>
fsck my_other_big_file (checksum...) ok
...

Use -S or --incremental to start the incremental check. Use -m or --more to continue the started check and continue where it left off. Note that saving the progress of fsck is performed after every 1000 files or 5 minutes or when --time-limit occours. There may be files that will be checked again when git-annex exists abnormally eg. Ctrl+C and the check is restarted.