Adding a lot of plants and other objects to the aquarium will help him feel more secure and block any reflections he might be seeing of himself in the glass. You should also check out the filter baffle tutorial in the betta habitats and accessories section--many bettas are stressed out by filters that produce a lot of current. Because of their long fins, and the fact that they are a still water fish, current can stress them out and cause rips and pinholes in the fin tissue.
Since you just added a filter, you should also research the nitrogen cycle. This is the process in which your filter is colonized by beneficial bacteria that break down the ammonia the fish excretes as waste into a less harmful substance called nitrate. Your understanding of the process and how to cultivate a bacterial colony will make it much easier to maintain your tank and keep your betta healthy.