The bouncing is usually the cable, and sometimes lubing the inner metal strand fixes a jumpy needle. (but it could also be the gear in the trans stripping)
Being off and hanging at a spot other than zero is usually a deeper problem in the unit itself.
There is a calibration spring and little lever on the back of most of them and it comes loose from the unit frame so the spring to return it to zero can't.
I just fixed one like that with a small dab of RTV where it needed to stay.
If by chance you are not up to that kind of stuff you will need to replace it or send it off for repair.
I'm sure one of these guys can recommend the place that does them, but I can't recal the name.