I know what it is. It happens when you're not using an expensive enough Beta machine. The office and screening products and I believe the 1800 don't correct for any tape errors like that.
Starting with the 2800 and working up through the more expensive decks, they deliver a fully corrected video signal. By the time you get to the 2650 play machine, you get dropout and velocity compensation, still-framing and reverse play with clear picture.
Yes, you can certainly make the problem worse with worn or distorted videotape or old heads in the deck. Those machines are full of rubber parts and they need to be replaced every so often or they, too, will start doing that as the tape pathway becomes damaged.
Sony has started to seriously discontinue the parts.
And yes, you're perfectly correct. It's called flagging. Everything inside a video machine is moving and it's a ballet. The first time somebody drops their tu-tu, the opera is over.
Koz