It has NOTHING do with playing for Roma, duels with Pavel or whatever arrogance you mean. Though he is hotheaded as HELL, and that ofcourse effects his game.
Last season he sucked BALLS, I seen his very error prone and headless chicken style defending since the start of his career, but he has just regressed further and further IMO. He is "good", but extremely inconsistent, he can go from decent to disastrous in the same game. Highlight example is too many (France NT chance a year ago, plays qualifiers against some minnow team, gets to starts, scores own goal and huge blunder for the other, utterly clownish performance), but anyone remember Roma's CL games against Arsenal last season? Mexes had one of the worst performances I ever seen a defender have. 90mins straight, and thats not uncommon for him, even in lesser degree then that.
His approach to defending can be pretty damn brainless and hotheaded (quite more talented version of Caceres type of "defending"). I watched Roma alot last 3 years, and the moments he has let them down has been quite prevalent. He was benched by Burdisso earlier this season for a bit, and there was a good reason for it, Ranieri got tired of some of Mexes errors costing them in the first 2 games.