Steering wobble 2004 Ford Explorer W/Rack & Pinion.

If the rack and pinion are new check the tie rod ends and ball joints, also check the steering idler if it has one .

if this has a conventional front end(not front wheel drive) then there will be one on each outer tie rod end one on each inner tie rod end, both upper and lower ball joints on each side, idler arm and pitman arm. if its front wheel drive it will have a rack and pinion steering. there for there will be one on each outer tie rod end and one on each lower ball joint, if they have grease fittings. so conventional steering has 10 fittings total and rack and pinion has 4 total.

There's no easy answer for this because it involves checking every joint from the wheels right back to the steering box/rack & pinion/steering servo. Start with tie rod ends and upper & lower ball joints. Hopefully you find your problem here because after that it gets harder and requires more info on the vehicle.

Could be loose lugs/ not torqued to spec. , bad wheel bearing, bad ball joint(s), bad steering arm joint, bad rack and pinion power steering unit, or other steering components. Check lugs first, loosen and retighten while slightly jacked up to take some pressure off of the wheel use a torque wrench set to 100 ft lbs. Then raise wheel about and inch off the floor, use a crowbar to pry up on the wheel several times while observing your ball joints for excessive movement. Very much play at all, replace ball joints, works better to replace them as a pair, top and bottom. If OK, raise wheel a bit further, and grab the top and bottom of the wheel and push/pull in and out to check for play in the wheel bearing. Pretty much any play, replace wheel bearing. If ok, do the same with a side to side motion while observing the steering control arm. Look for play. Play in the joint, replace joint. Play in other steering components, replace suspect component. That's about all the stuff could make the wheel wobble unless the rim itself is bent.

Are you referring to the rack and pinion steering assembly? If so, repairing or rebuilding this unit requires very specialized tools. Even auto repair shops do not fix these. We simply remove the defective unit and replace it with another good complete unit.
If you are asking how to replace this unit, that also requires special tools to remove the tie rods. You must also be very careful and know what you are doing or you can ruin the clock spring for the driver's side airbag. The shaft for the steering column is "phased" to the shaft on the pinion gear. You must be sure to keep the steering column and the new rack & pinion assembly in phase or you can do more damage to your truck. You will also need to take the truck to a shop for a front end alignment after you are done. If you think that you have the skills to handle this job, I would suggest you watch the videos I've linked. FYI, it will take a skilled mechanic with all the proper tools over 4 hours to do this job.
Rack Pinion power Steering Rack and pinion Replacement ford explorer part 1

Automobiles: 2006-2007 Ford Five Hundred 2WD & AWD, Montego

If the steering is getting a little hard to turn at low speeds, this would indicate a loss of Power Steering, and the steering is reverting to "Non-Power" steering, just like the days of the Ford Model T or Model A. Loss of power steering is usually caused by low level of PSF (Power Steering Fluid).
So first on my checklist would be checking the PSF level in the reservoir.
Also bleed (air) from PS (Power Steering) pump.

The Ford Five Hundred has front MacPherson struts, so check these for leakage (of the dampening fluid in the strut cylinder), or breakage of their coil springs.
These springs can actually weaken over time, but this is impossible to see - you must "feel" it by bouncing the strut up & down - preferably with your hands on the top of the strut tower in the engine compartment (rather than on the exterior finish).
If the MacPherson struts have weak/broken springs, these components are not separately serviceable, and the strut would have to be replaced as a unit (and preferably both left/right to maintain smooth/even ride).

The Five Hundred also has rear shock absorbers with springs - check for leaks/breakage/weakness here too.

Steering losing responsiveness/wander - checklist
Priority Action Part Type Cause
1 Inspect Rack & Pinion - Center Wear From Internal Fluid Leaking Around The Rack Piston.
2 Inspect Steering Stabilizer Bracket - Loose or Broken Steering Stabilizer Bracket.
3 Inspect Front Lower Control Arm - Front Lower Control Arm loose/missing bolt(s)
4 Inspect Front Lower Ball Joints - Front Lower Ball Joint(s) Worn/Loose
5 Inspect Front Upper Ball Joints -Front Upper Ball Joint(s) Worn/Loose
6 Inspect Tire Pressure - Tire Pressure should be 35 PSI for the Five Hundred and Montego's P225/55R18 OEM (Original Equipment Manufacturer) tires.

Harsh ride - checklist

1 Inspect Rear Shock/Strut - Shocks/Strut failing/leaking.
2 Inspect Front Shock/Strut - Shocks/Strut failing/leaking.
3 Inspect Coil Spring - Incorrect Coil Spring Selection or Installation.
4 Inspect Coil Spring - Coil Spring broken.

upper or lower ball joints are a possibility others are rack and pinion or even strut mounts

You have to get it aligned at a shop after messing with your steering geometry. Your tires could be pointing in towards each other or pointing out away from each other. It's called toe in or toe out.

Sounds like a serious front end problem, probably one or more of the components are shot, or if equipped, the rack and pinion steering. Better have it checked before something breaks and you loose the steering altogether.

The ball joints are pressed into the steering knuckles. To remove them requires use of a ball joint press. If you don't have one you can usually rent one from a major auto parts retailer. You'll have to remove the brake calipers, rotors and backing plates. Disconnect the tie rod ends, and remove the upper pinch bolt. The lower joint has a nut that holds it to the axle that must be removed as well. Use a ball joint separator or "pickle fork" tool to separate the lower joint from the axle. Once you have the steering knuckle in hand, remove the snap ring from the bottom of the lower joint. Use the press to push the lower joint out then do the upper. replace the upper joint first using the press then do the lower joint in a similar fashion. Installation is naturally the reverse of removal. One thing to note is that the upper ball joint is located in the axle with a bushing. This bushing is where caster and camber adjustments are made. the factory presets these measurements using a bushing with a tab on it that locates it only one way in the axle. If the vehicle has ever been aligned and caster and camber adjustments were performed, the factory bushing will have been replaced with an aftermarket bushing. These bushings are rotatable and care must be taken to note where they were indexed in the axle. You should probably still get the alignment checked though, as suspension parts will tend to settle, and steering angles will change. Hope this helps.