That's part of what makes him human. That's pretty much what the whole movie is about. It's easy to bend/break the rules to nail an obvious bad guy, but than you have a probable bad guy, than a guy who might be guilty (and even if he's not he shouldn't be hanging around with those guys anyway) ect. That's what makes him an interesting character; he grows and changes throughout the movie.

While I believe you have a point, Hub did NOT throw the money into the case, Agent Frank Haddad did.

Initially he tries to do things right, I think it is part of his character's decline driven by the events of the movie, until his redemption at the end to once again uphold the law using a court order, rather than just running in with a gun as he did at the school.