One of the goals of a pick and roll is to try to get defenders to switch so that you get mismatches such as a guard like Avery Bradley finding himself against a big man who can shoot over him. AB ending up guarding a player like Chris Bosh one-on-one is pretty much the worst outcome.
The Celtics (and the Bulls) play a complicated form of pick and roll defense. As I understand it, Bradley is supposed to chase the ballhandler. The guy guarding the pick-setter is supposed to help on the ball-handler, a third player rotates to help on the screener, and the other two players protect the passing lanes. Bradley's job is to follow the ballhandler, who is temporarily double-teamed. When Bradley catches up to his man, everyone can rotate back to his original assignment. Bradley (or Rondo, for that matter) is fast enough to close in on an opposing point guard before he can stop, plant, turn to face the basket and get a jump shot off. If he drives, the player originally guarding the screener (usually a big) is in his path to contest a layup. The easiest pass to the open man is usually a long pass which will allow the Celtics defense enough time to close out on a jump shot.
If the screener is getting open, the problem is that a third defender is not rotating properly. Another problem that can occur is if the screener's defender doesn't trust the third player to rotate properly and doesn't double-team the ballhandler properly. These are the sort of defensive failures that probably lead to Doc Rivers leaving rookies on the bench.