Why is my Busch Pressman rangefinder horizontally misaligned?

The images should be aligned horizontally. It's difficult to imagine the rangefinder mechanism becoming misaligned yet remain working, and the ocular optic is common to both halves of the system. That means that either the main primary (the "whole picture" view system at the end pointing to the subject) or the periscope (the rangefinder) primary has become misaligned. Luckily, that means that you won't have to monkey with the mechanism at all. My first thought would be to look for any signs of damage to the unit near the primary lenses; if a slight ding in the box has caused one of the lenses to shift, you'll know which one to work on and how to go about fixing the alignment. If it's a matter of one of the mounts having slipped, that should be easy to spot as well. There is a chance, though, that it's the cement holding one of the primaries in place that's the cause (due to age or heat at some point), and that may not be so easy to spot. It may make sense to remove both, clean up any existing cement, and recement the lenses.