Off of 1 panel I have:
3 220V circuits
4 110V circuits

When one of the 220V breakers is on, all the 110 circuits display some
kind of "error" -- either hot/neu reversed or hot/grn reversed, or in
one case all 3 lights come on! (which is not suppose to be an
option!). It's the same error on each circuit, just different errors
depending on which circuit it is.

When I flip off that one 220V break, all the circuits read fine.

What could it be? The 220V circuit has 3 outlets on it. And they all
work.

The 220V circuits use 3 wires - black, white, ground. Black and white
go to the breaker.