I heard it was the timing of his recruiting. He was soliciting staff and players about to become free agents like Matt Chatham while still on the Pats staff and before he accepted the Jets job. That is bad business no matter what industry you are in. It violates the NFL tampering rules too with players not yet into free agency. I think the Branch tampering was the straw that broke the camel's back.
I know the media painted Belichick as the bad guy in this, but I can see how he can act like he did. Belichick made Mangini. Not that Mangini isn't a talented coach, but Belichick took Mangini under his wing probablly due to the Welslyan ties. Mangini repaid him by trying to rob him of staff and players while taking a paycheck from him.
No wonder why Mangini was barred from the Pats facilities after he got the offer from the Jets, but hadn't taken it. Crennel wasn't barred and he took a few key staff members (Jeff Davidson most notably) with him. There appears to be no animosity between Belichick and Crennel. So eventhough the press likes to portray this as one sided, there is definitely blame to go to Mangini.