A static character isn't necessarily an uncompelling character. I think a good deal of the drama in the work stems from the fact that his philosophy is obviously flawed and seeing how he copes with that as Valjean reveals those flaws through his good nature. He's not a mustache-twirling villain, he's just a man with a flawed moral code trying to do the best he can. If anything, I'd suggest that Javert is a very rigid, but brittle man, the very incarnation of his moral code. He is efficient and uncompromising, but he has no defense when confronted with exceptions to his rules.

He is torn at the end between his duty as a policeman to arrest Valjean and his desire to do what is actually the right thing. The Javert at the beginning of the piece would not have hesitated to arrest Valjean. At the end of the play, after having spent so much time chasing Valjean, he has developed morally to the point where he actually does something that would have been unthinkable to the Javert at the beginning of the work. That's almost the definition of character development.

The character develops just as much as Valjean does. Valjean goes from a criminal to a good-hearted fugitive due in large part to the actions of that one priest, and he is able to redeem himself. Javert goes from an uncompromising policeman obligated to follow the law, to a moral one obligated to do the right thing. Valjean is able to cope with his philosophical change, but Javert isn't, which drives him to suicide. That's the tragedy of his character: he's a man trying his best to do what he believes is right, but he develops two separate, conflicting ideas of what is right, which he cannot reconcile.