Foul Tip/Foul Ball
 

I just saw a very bizarre play happen on TV in an MLB game. The batter fouled one off, and it immediately hit the catcher's mitt. The catcher failed to catch it, and the ball bounced straight up on top of the batter's shoulder. The ball sat there for a few seconds and then rolled off. The very puzzled looking batter caught the ball in his bare hand as it rolled off of his shoulder and handed it back to the plate umpire.

The plate umpire was giving the regular strike signal up until the point when the batter caught the ball, and at that point, he threw up both hands to signal foul ball. I was not paying enough attention to know if it was a 2 strike count at the time, which would of course be the only time it being a foul tip vs. foul ball would matter. But, the defensive manager did come out and have a brief discussion with the plate ump.

Would the defensive manager have any kind of case for claiming that the batter interfered with the possibility of it being a foul tip and third strike? If it matters, the batter definitely did not intend anything. He had an incredibly puzzled look on his face as the ball rolled off his shoulder and just instinctively grabbed it with his bare hand.

No. For it to be interference on a foul batted ball, it has to be intentional.

I don't think a foul tip call is in order if the ball touched the batter after touching the catcher's mitt.

As soon as it touched the batter it became a foul ball, no foul tip possible.

And from my understanding from another recent thread, it could not have become a fly out, because it did not rise significantly in its trajectory from the bat to the mitt. So the umpire's signal might've been a little late, but better late than premature.

You'll get no argument from..., well, anyone.

foul tip caught vs foul ball caught
 

What is the legal definition of a foul tip versus a foul ball that is caught. How high does a batted ball need to be, to be ruled a foul ball that is caught for an out?

A "foul tip" is "sharp and direct."

Anything that's not "sharp and direct" is a foul out. No specific minimum height ("above the batter's head" is a common myth)