A major point of failure in a full recovery model is not testing your backups. You should not limit this to your FULL backups either. If you have full recovery model on any of your databases there is more than likely (or should be) log backups being run based on either DR strategies or transaction log management. If you also have differential backups to take full advantage of the quickest path to restore, then all of these stages must be tested out.
Key points
Test restoring full backups
Test applying differential and transaction log backups
Check header information on all backups. To do this you can submit to a table for historic purposes the results from RESTORE WITH HEADERONLY, "RESTORE HEADERONLY FROM DISK = BackupFile.bak'"
Push testing further than one time restore. Automate your RESTORE tests either daily, weekly or what your resources permit. Remember, just because you go on vacation does not mean your methods change and your duties go away.
Document the results and let management know of those results with either simple reporting results of