My mixer is a lift-top and the top seems to be loose and wobbles as it mixes. help?

The locking portion on the stand may be loose, misaligned, or wearing out. Or the bottom of the bowl needs attention.
It shopuld never move when mixing.

I'd be looking at making sure the beater is not banging on the bowl and that the head hinge isn't loose. The bowl is secure on the base with this system that has been in use for decades so you are looking for a fault not a re-design of the system. The friction of the mix in the bowl should logically tend to tighten the bowl, not undo it. I have seen a malformed bowl once where the lugs weren't big enough and I suspect that it's possible for there to have been the odd malformed bottom plate with not big enough lugs.

If the base is not holding the bowl properly then only a replacement base plate or another bowl is going to fix it. The base plate is held onto the pedestal with 3 Philips head screws.

I had the same problem.. not the top plate, but the whole head was wobbly. I fixed it by removing the top plate, then locating the three screws that hold the top to the base. These screws are under the motor. I had to remove the motor, but this also required taking the transmission cover off. Sounds harder than it really is. Once I tightened those three screws, the play went away.

Turn the mixer over and look up where the pin goes through the two pieces. There is a screw there which secures the pin. Tap the pin into position and tighten the screw.

the solution to this is to tighten the screw visible through the base that intersects the pin. Turn the machine upside down and using a long flat screwdriver tighten the screw.

More likely the pedestal base is bent. Your local service agent has probably seen it before and should be able to bend it back flat again. It's a brutal process with a heavy soft hammer that you probably won't want to see.

Remove the back housing by removing one screw and liftingand pulling rearward.
Remove two screws holding the metalic edge trim. This uncovers the seam. Screws are on the back.
Remove four visible screws from the bottom of the head around and near the pillar.
Now gently using a screw driver, push the metallic ring on the mixing head down and off.
This uncovers five more screws about the mixing head. Remove them.
Using a very small screw driver or punch, puch the pin out of the mixing head shaft.
Remove the mixing head housing.
Lift up on the motor housing to remove it.
The motor/gear housing is the top protion of the mixer. Its loaded with grease so do this over a covered countertop or some place easy to clean. The grease won't run, but it can fall out in gobs.
Make sure all sealing surfaces are clean, especially the gasket around the gears. This will insure a good seal. No gear grease in your famous cookies!
Reinstall in reverse.

Do not store or transport the mixer on its side ever. Always upright. The grease in the gearbox should even out eventually. Try sitting on it when it wobbles. At least yours works.

The "wobbling" sounds like an issue of beater to bowl adjustment, which can come out of alignment naturally over time and with use of the machine.

If the flat beater is striking the bottom of your bowl, this may cause the locking mechanism to loosen and may cause the mixing head to "bounce" during use.

Your Use and Care Guide will cover the "beater to bowl adjustment," which you can do at home in a few minutes with a flathead screwdriver.

Also, leaking of oil in a stand mixer is not necessarily indicative of a large problem.

Kitchenaid stand mixers are overpacked with oil to last the lifetime of the motor. If the motor sits idle for some time (is not used), the oil may begin to drip from the gears and settle. Oil leakage may primarily be seen from around the beater shaft or planetary action.

A stand mixer can lose up to a 1/4 cup of oil before it needs to be serviced.

It is recommended to run the mixer on speed 10 for 2 minutes in order to redistribute oil back into the motor. In order to prevent future occurences, this is recommended to be done every 3 weeks if mixer is not being used.