[CecilOne]

Originally Posted by Big Slick

Part 1:
Why is PU watching the (flight) of the ball? PU should have eyes around ground level; the fielder will take you to the ball (do you watch a foul ball the catcher catches?). Staying on ground level allows for you to watch leaving early, possible interference (if a fly ball in the infield), and your partners chasing (or not chasing if that is part of the mechanics) in three umpire systems.
Agreed. Not flight going out, just noting ball near temp fence and looking for the incoming throw.

You didn't mention if this is a possible catch or line-drive/base hit. If this is a base hit, why is there so much focus on the ball?
Base hit.

Part 2:
Why is PU so concerned about R1 scoring/touching the plate without a play? That is something you can give a glance to while you are in the holding zone or on your way to third.
Not "so concerned", just normal watch, apparently overdone.

Part 3:
Why is BU, who started by F6, not giving some attention to the lead runner(s)? Even in two umpire system, with a runner on third, I look ahead to third base as I'm moving inside to pick up training runners (including batter/runners).
No reason except habit. I hope I'm will be doing what you said (bold).

All of your concerns are about both of us doing something wrong.

Summary: umpires must be aware of developing plays, including cases where possible obstructions can happen. With multiple runners, umpires must pre-pitch and be aware. Either umpire should see this.
Yes, definitely a mistake.

Thanks!