Only other examples I can come up with, but could have mentioned:
-Alfonzo Dennard. Pre-draft incident where he got into a scuffle with a cop, apparently. Ended up with community service, I think, and it was before he was drafted. Main reason he was drafted in the 7th round vice being a 3rd rounder or so as projected.
-I think Talib had issues a few years back, when he was with the Bucs. Kept his head down with the Pats so far, and they only gave him a 1-year "show me" type contract to see if he can keep doing it.
-There was a special teams guy a few years back that got busted for selling pot out of his car. Forget who, but was a fringe-type player, and was cut.
-Think Kevin Faulk got popped for smoking weed at a concert a while back. Was away from the team while rehabbing an injury (his knee, maybe?).
That's really about all I can think of off the top of my head. that it's that short a list, and minor stuff, is already an improvement over most teams. Something like 35 NFL arrests over the 2013 off-season (only 20-something unique players, though, that one idiot got arrested like 3 times in a day or so!). Players come from some rough backgrounds (violence or just poor), so can be tough to plop them in a situation where they get rewarded for it with more money than they can handle, seedy elements around them, and then need to turn the violence on and off at game time.
Patriots certainly aren't saints, but think they do better than most at keeping their heads down. As they've gotten further and further away from a Superbowl ring, and keep looking at the window for Brady and Belichick getting smaller and smaller, they've been straying a little from their principles at times to try and get another ring. Means taking more chances on character guys because they have the big game skills, drafting guys that slipped because of it, or trying to make reclaimation projects out of guys with problems, hoping a short contract and change of scenery will pull them through. Had SOME success with that, but it's not perfect.
And like I said, one of the bigger pieces of that media-created Patriots Way thing is just not running your mouth, letting your play speak for itself. They don't trash talk, they don't do a lot of media interviews, and frankly sound like programmed robots when they do. 'One game at a time, do what I can to help the team, etc.'
Much of this really came around when they had guys like Vrabel, Bruschi, and McGinest on the team. THOSE were the kinds of players they are thinking of when they spout off about this myth. Some of that ethic is still there, but not as strong as it was then.