The most important issues here would be his inability to lead a team as proven by his track record, being the main catalyst in firing a coach and of course being a locker room distraction with all his antics...in short he can destroy a team rather than uplift it to a championship.
The criticism of a player's inability to lead a team can be addressed to just about any superstar who's been in the league for a while and hasn't won a title (Deron=coach killer, Melo=leadership issues etc). Same with character, injury, and other issues. They're there if you nitpick hard enough. It doesn't mean that they're not worth trading for.
Even Olajuwon had somewhat similar issues as Dwight (asking for trades, even suspended for faking injuries) yet he won two titles with the Rockets after the debacle.
If he gets traded to another team this year what's the assurance of that team that he will sign a long term contract? Nada. The guy could just disappear after this year is over.
Well he already said that he would re-sign with Brooklyn. As for the Lakers, Bynum is also expiring. Where's the assurance that he's not gonna bolt next year?
If you are a GM will you trade for him? If yes then good luck to you.
Luck, everyone needs it.
EDIT:Apologies, my reply disappeared the first time for some reason.