From Documentation/md.txt in the Linux kernel documentation:
clean - no pending writes, but otherwise active.
When written to inactive array, starts without resync
If a write request arrives then
if metadata is known, mark 'dirty' and switch to 'active'.
if not known, block and switch to write-pending
If written to an active array that has pending writes, then fails.
fully active: IO and resync can be happening.
When written to inactive array, starts with resync
So, no, you don't need to worry about either state; both are normal operation. If you saw
inactive, that you'd have to worry about.
mdadm includes a raid monitor daemon that will alert you (via email by default) of any conditions you need to be aware of, in particular a failed disk. You should make sure it is configured & running.