PC-screen
 

How about the dribble-handoff a lot of teams run with their motion or flex offense? Many times that play looks a lot like a moving screen to me.

Assuming the "moving screen" to which you refer is illegal, you should call it until they stop.

It can be. One that you'll see occasionally is where a A2 curls around the A1 (who is holding the ball). As A2 passes A1, A1 pivots into the path of B2 who was guarding A2 and while passing the ball to A2 who is now heading down the lane for an undefended layup. It gets missed more than it is probably called, but that is an illegal screen.

Could be, assuming there is contact; but quite often A1 pivots and continues to move (roll) anticipating a possible return pass. In these cases I would think A1 is no longer screening and the contact most likely would be incidental, would you agree?

This play would have to be judged on an individual basis. But intent is not the main concern here. Even if A1's movement is in anticipation of a return pass, if in doing so he hip-checks a defender and hinders his progress he can still be called for a foul.

If A1 pivots and, in doing so, knocks B2 off of A2, it IS a screen no matter what A1 wanted to do. Usually when I see this, it was contact that freed up A2 who is now going down the lane with the ball undefended.

I agree with that situation. However, most often when I see this play A1 pivots out of his screen soon enough to block the defender's path (the defender is momentarily caught behind A1) as A1 continues his roll toward the basket. The defender, either surprised or not wanting to cause contact into the back of A1 stops or adjusts his path and there is no obvious contact so play on, correct?

Right, if while pivoting A1 contacts B2 we've got to call something-if not an illegal screen then charging. But as I replied to JAR, in our area players seem adept at pivoting out of the set screen early enough to block the path of the defender without causing contact. When I was in high school and when I coached we ran a "shuffle" offense where the wing opposite the ball would cut off the high post and if the defender tried to go around underneath, the post would pivot right into his path and keep right on going toward the basket. Never once had it called; but then how could it? The sudden pivot caused the defender to hesitate which is all the cutter or dribbler needed.

Correct. A little information is a dangerous thing, and this is an example. Many coaches yell "Moving screen! He can't do that!" But there was no contact, so there is no infraction.