Dave,
Don't know if this will help, but my older Craftsman had a lever on the left side of the post that would allow you to "preset" the position of the head to 90 degrees after you had moved it to another angle. The lever would drop into a groove that was supposed to bring you back to a perfect 90 degree cross-cut. Located on pivot of that lever were two adjustment screws that let you fine tune the angle so that it was exactly 90 degrees when the lever dropped into the slot. Those adjustment screws also let you take any slop out of the arm.
Also, can you tell if the side to side movement is in the saw head itself or in the arm? The Craftsman that I had also had adjustment screws that would allow you to adjust the play out of the rails that the saw head rode on as you extended and retracted the head. Look around and take off any covers that you see around any of the articulating areas of the saw. Most of these saws have adjustments in them. If it is not a new saw, try taking it apart to ensure that saw dust has not built up preventing the head from seating in areas that rotate.
Good luck. There are a lot of areas on a radial arm saw that can get out of adjustment. Hope that you find yours and it works well.