He goes after the Lizard on the bridge because his spider sense goes off. I doubt he's even aware of exactly what's on the bridge in the first place--he goes because he senses the danger.
Did you forget the scene on the bleachers??
Peter: Whatever that thing was on the bridge, it could have killed those people. I have to stop it.
Gwen: That's not your job.
Peter: Well, maybe it is.
This is all before he learns that Connors is actually the Lizard. His sense of duty and responsibility are very much intact. And what's wrong with attempting to take pictures of him fighting the Lizard to make some money?? This has been seen in multiple iterations--Peter taking pics of himself in action and selling said photos to the Bugle. In SM1, Peter takes pics of himself stopping those guys robbing the armored car--how is it any different in ASM? It isn't.
Completely agreed. That combined with the excellent voice cast/acting and the brilliant story telling, it's the best animated show by far. The only downfall is the series was cut way too short. And knowing what plans Weisman had for the show, had it continued, only makes the cancellation that much worse.