Dez is one of the 5 or 6 most physically gifted receivers in the league. Huge hands, dynamic running ability (look at his punt return history if you don't remember), great size, very strong so he's almost impossible to jam at the line of scrimmage, and so forth and so on.
The downside is not just his behvaior, but also his lack of basic football intellect. He doesn't know when to break off a route if the coverage is zone. He's rarely on the same page as Romo, and I'm guessing it's his fault because Romo seems to always know where his other receivers are. He's not as effective going over the middle as he should be (given his strength). He quits on routes if he's not the first option (I'm not sure about this, but I've seen Romo miss him badly if he's not first or second in the progression, so I'm assuming Bryant isn't running those routes very hard). I don't know what to make of him.
The off-field stuff is fine if a player produces (how long did Minnesota put up with Randy Moss?). But these other things are preventing him from being elite like Larry Fitzgerald, Megatron, and Andre.