How serious is the problem of "stopping too far" next to the jet bridge?
I can't tell you how often it happens, but the procedure is quite simple: stop the aircraft immediately, and alert the ground crew. It is then up to the ground crew to decide what, if anything, needs to happen. If the aircraft has just slightly passed the intended stop position, maybe it can just stay where it is. If it has overshot significantly, it may be required to push the aircraft back to the correct position with a tug. Worst case, the aircraft might have actually hit some obstacle (building, vehicle, jet bridge) in which case the aircraft or surrounding equipment might have been damaged.