As permanent item I would agree and say the mirror is a bad idea, it will stress your guy out and if he decides to start attacking it because the "enemy" isn't going away, he might even possibly hurt himself.
I have found that using a compact mirror for very short amounts of time works just fine, and you don't necessarily need to put it in the tank. None of my bettas have never had an issue with seeing the mirror through the aquarium glass.
A couple monitored minutes to get them to flare and do the little dance. Once or twice a week it has always made for a very happy betta in my tank.