If you look the newest Heat member up on basketball-reference.com, you will see that Bibby is a very good offensive player, a very bad defensive player, an outside shooter who is deadly and a guy who has a 2-1 assist-to-turnover ratio or better.
The only real change over Bibby's entire career is that he used to shoot more free throws and he used to be a little better assist man.
So, that said, what do the heat need him for -- to fill the Mo Williams and Booby Gibson role of "wait out by the three and we will get you the ball six times a game." Stats say Bibby will hit 2 or 3. The Heat just hope it is 3 instead of 2, and that some games it is 6.
Conclusion -- good signing, certainly worth a shot.