A USB disk is treated pretty equivalently to an IDE or SATA disk in this respect. As long as the OS is shut down cleanly then blocks will be flushed and I/O completed. So it's safe from an OS perspective.
Note that cheap USB flash drives may not survive, because the cheap ones aren't designed for high activity. But a hard drive connected via USB should be fine.
The OS automatically detects if the disk wasn't cleanly dismounted and will check the filesystem. It can also be configured to periodically check (see `/etc/fstab` and `man 5 fstab`) on reboots.
A disk can be checked for bad blocks with the `badblocks` command. Be carefuly about using it on a disk that's in active use, except in read-only mode