Impact of changing instances' passwords
Well for security reason you should not be letting anyone use the "sa" account. If you do then obviously changing that password will break whatever is using it. I try to set this password to a random password, rename it (only SQL 2005 and above allow this), and then disable it. I have not found anything so far that explicitly requires the "sa" account to function, my own admin account suffices.

With regards to the service account this should not cause any problems. Again as long as no other resource or service is using the same account.

The only backup plan I can suggest is having the old password handy to reset the accounts back to in the event something breaks.