You have to evaluate each guy, and not group all the 'character' issue players together like they're all the same and will behave the same way. Dillon's issues were different than Moss, Moss's are different than TO.
Both TO and Dillon, especially Dillon, worked hard. TO is nuts, Dillon was bitter, those were their character problems, but they did go all out on the field (except maybe not TO as much in Dallas in the end, but again, crazy guy). Dillon was fine when he was winning, that cured his bitterness, and there is no cure for the TO brand of crazy.
The knock on Moss is that he's lazy. If he works hard, does what Brady wants him to do without complaining or whining, does not give up on routes or show up his QB if he's not getting the ball....there will be no problem. I am not worried at all about off the field issues, despite some incidents in the past, Moss is not Pacman. It's on the field effort that is his 'character problem'.
I think like with Dillon, winning will cure a lot. In terms of the media, Moss can avoid them like Dillon did, I don't care, maybe that would help.