There's another experiment that should be tried. Rotate the whole apparatus 90 degrees and see whether the midpoint of the rotation moves with it. If the bolt (the electromagnet) is not exactly plumb, or part of the return flux path is through nails in the frame, then there's a bias in the...
Just noticed that when the washer is nearly parallel to the light beam, it appears to oscillate laterally in translation, seemingly in the plane of the washer. I can't tell whether this happens during other portions of the rotation cycle. A time-varying lateral force must be causing this...