Is there an easy way to find all stale mounts on a system?
Just use the df command. It will not be able to report statistics for any stale mounts. If you have a lot of stale mounts, this will be time-consuming. But you asked for easy, not fast. 
it depends on the system, in AIX for example you can use SSA manager to see the stale volumes. You also can try netstat to see UDP streams with stale timestamps and then netstat it for a command it uses, and then use lsof to trace the files ( so the filesystems).