Monitors use electromagnets to steer an electron beam. The earth has a more or less constant magnetic field in a certain orientation. Rotating the monitor changes the magnetic flux the electron beam experiences and might distort which subpixels the electron beam is hitting.
I had a Samsung 19-inch pseudo-flat CRT that showed discoloration in the corners just by rotating it horizontally. Turning it off and on again fixed it (I supposed it degaussed on startup).