I would guess that your shifter mechanism in the center console is worn out. There are a few threads on here showing that the steel bases crack and/or the bushings in the pivot holes wear out.
As for not staying in the apparent reverse location, the four speed shifters have a special lock-out gate to ensure you don't accidentally put the shifter in reverse. It's really just a spring loaded ramp. The part of the shifter mechanism that rides up that ramp wears out after a while and can make the shifter flop around while in reverse. This might be your problem, but I'd be more inclined to think your bushings are worn out since you've got problems in all gears.