His constantly accepting and securing bribes from unsavoury people while in office was notorious enough that when he declared while shutting down Fat Tony's rat-milking operation that "the Mayor's office is not for sale", the reporters proceeded to laugh at him, apparently the irony of his statement not being lost on them, causing him to request and fail to have the laughter edited out.
If bending the law will suit Quimby's purposes, he will likely do so.
He once arranged Marge Simpson's release after she was arrested for blocking traffic on a bridge after suffering a nervous breakdown, claiming that if she went to jail, Quimby could kiss the "chick vote" goodbye meaning all the women in Springfield would hate him and no longer vote for him since Marge's reason for blocking the traffic was understandable.
He also resorted to bribing witnesses when assault charges were brought against his nephew, leading Bart Simpson to observe that "the system works: just ask Claus von Bülow". He is also willing to do corrupt things when he is confident that he would not get caught.
Ironically, he actually did attempt to spend quality time with his wife when his life was threatened by Fat Tony after he (albeit forced to by Homer, his bodyguard) shut down his rat milking operation when Homer tried to invite him out to avoid concerns about the mob.