I'd probably add a step at the end.

After the applications are up and you're sure they're all pointed at the new server and working fine, bring the old database back on-line (or restart the old SQL Server), and perform a final full backup. This is useful for ensuring you have a copy of the database as it existed in its old environment at the time of cutover. As you noted, sometimes the new database may not be restorable on the old server (different SQL versions). And depending on auditing requirements, you may need a restorable backup for off-site storage. It also gives you a picture of the data as it existed at the point of cutover.