The most noticeable flaw is related to the shooting guard hole, and was the one roundly exposed by Miami. In their current guise, Chicago has only one ball handler, Derrick Rose. And if you take the ball out of his hands, Chicago has no other options.
Ronnie Brewer cannot dribble, and nor can Keith Bogans. Deng has never been able to do it unless he is playing for the Great British national team.8 C.J. Watson is a decent backup point guard on both ends of the court, and yet strangely, for a point guard, his handle is not great. You can therefore make a legitimate claim that Chicago's second best ball handler last season was its starting centre, Joakim Noah, the hands-down best player on the planet. But this is not much of a virtue, because unless it's his patented driving lefty layup high off the glass, Joakim is not in a position to do much with his ball handling ability, considering that he is no threat to make a shot from the perimeter.
Miami exposed this flaw by either double teaming Rose, or smothering him with bigger defenders, or both. When forced to give the ball up, Rose either turned it over on the jump-pass (which he does rather a lot), or gave it to someone who was quickly contested and who could do nothing with it. Chicago, therefore, lost its entire halfcourt offense.
Furthermore, Chicago struggles with shooting the ball from the outside. At the angry behest of Tom Thibodeau. Deng has mercifully turned his 22 footers into 24 footers and become a decent three point shooter, while Derrick Rose completely re-designed his jumpshot technique last summer and came out of it with a three point stroke that was a slight improvement on what went before it. (Although somehow, in the process, he lost his previously elite mid-range shot. All in all, a mixed return.) Ronnie Brewer can't do it, except, seemingly, for in the fourth quarters of playoff games. And C.J. Watson, the best 37% shooting backup point guard in the league, had a decent year with his flat-footed high arcing bombs, but hit only half a three a game. (If that makes sense.)