The rear of my 97 Crown Vic is producing a wobbling sensation that is also causing my steering wheel to rock left and right slightly. What are the possible issues that can create this effect?

I suppose it is possible - almost anything is possible with motor cars. Like the old saying goes; anything with tyres or testes is going to cause trouble sooner or later, however, I have never known the symptom you describe to be caused by a transmission.

I have known an unfortunate choice of tyres to cause some strange sensations. Some of the early Michelin tyres used to wobble a lot under acceleration. I have known some older tyres to sometimes feel like the wheels are walking along the road rather than rotating but that was at a fairly low speed and neutral throttle opening.

Worn driveline components are by far the most common causes of a less than smooth power delivery with worn inner drive shaft joints the top of my list for strange or unusual wobble sensations.

It is wise to go back to basics and do some serious checking before spending any money...

indicates failing or incorrectly adjusted wheel bearings
contrary to popular belief wheel bearings have to have a slight preload adjustment to
a-- keep the oil from leaking out of the bearing seal
b--- compensate for the gyro action of the wheel ( flywheel ) when the plane of the spin is altered ( changing steering direction)
if the bearings are not correctly adjusted the wheel will develop a wobble similar to what a top develops as it slows down roads that have a high crown require a different wheel alignment setting for the camber so a wheel alignment may be in order
check the tie rod joints as well but normally a bad ball joint will cause the wobble in the straight ahead position at speeds approaching 30mph or better

A bent rotor or a stuck piston in ur caliper either from dirt in caliper or a bad your brake hose. Thats what I'd say were the most likely causes and if you don't feel a wobble I'd say the caliper on one of your wheels. chk ur pads if 1 set is worn a lot more than the others or an excessive amount of brake dust on 1 rim that could be your culprit. Hope that helps.

I am going to use a Crown Vic as an example because we do not know what type of vehicle you have. On the Crown Vic there are rear stabilizer bars(sway bars) which go from one side of the body to the other. On each side there is a bolt with many rubber bushings which are meant to prevent the car body from shaking and rolling in turns.

Looking from the back of your car you will see the bar hanging down before the rear axle. One side, if not both sides have broken bolts. They are called suspension links and they are readily available at autoparts stores. You also have similar sway bars in the front. The front set bolts to the frame in a different type of mount.

You can have bad shocks or struts, moreso on one side as you indicate the problem is with left turns. On the extreme condition, a balljoint or tierod end can cause sloppyness in the body on turns.

There are some differences with rear suspension on front wheel drive cars and AWD vehicles. But is you see a bar underneath your vehicle just check out if it is still attached. I hope you found my solution very helpful and would be interested in your outcome.

Have the rear wheel bearing checked and check the outer tie rods checked for play.

Check the transmission linkage cable that runs from the steering column under the dash to the trans under the car. make sure that the cable is not damaged and that all connections are tight.

Over time those SS steel cables stretch. Most of the older Fords have an adjustment in the cable just before it splits into 2 cables running to the rear wheels. Should be a easy find.
PS. Don't over do the adjustment... a bit of penetrating oil the day before the attempted adjustment will make the job MUCH easier....
Hope this helps.

try turning the steering wheel left and right while turning the key, sometimes when you park with your wheels turned it will lock the wheel and key. you may have to put a little force into turning the wheel, nothing that will make u sweat... hope this helps you and good luck!!!

What rims are on the car the steel police ones and what tires are on it could be hitting the stops on the frame and where the proper bolts put back in on the rack mounts and did you go with the heavy rack for the police car .Cause when I built them there was an issue with the proper bolts and there was a different rack for the cop cars the to the basic crown vic do to the suspension upgrade on it and the diffrent pump