Auto gearbox - when we bought the car in August 2000 it was not selecting gear properly when going from Park to Drive, slipping between changes and stalling at lights. This was fixed simply by changing the autobox fluid and filter.
I have also just fixed a seemingly common and very frustrating problem with the gearbox - never getting 4th/overdrive and also having to shift it manually into 1st to get it.
The problem on my car was not in the actual gearbox at all, but the Transmission Control Module (TCM) part # 56027316 which is located under the dash above the brake pedal. It is a 2-minute job to change and your Jeep technician should be able to diagnose it in 30 minutes with the fault code reader and service book. I got a used one for $100. The symptoms were it turns out, "limp home" mode where the TCM just uses 2nd and 3rd gears when in Drive.
Also Note: it seems that many owners and even technicians do not realise how sensitive the 42RE gearbox is to the type of auto fluid used. The hand book states that the more expensive Type 7176 should be used and not the regular Dextron III. Ignore this advice at your peril.
Tires - Cooper Discoverer 225/75R15. We had a front tire lose the complete tread at 80 mph. It ripped the wheel arch liner out, dented the sill and fender and broke the turn signal lens. My wife did a great job stopping the vehicle in a controlled manner. I am always very careful checking tire pressures and several hours after the incident there was still 30 psi so the loss of tread was not due to under-inflation. Many Jeep-owning friends have also had problems with Cooper Discoverer tires.
Quadra-Trac - permanent four-wheel drive transmission with viscous coupling on centre differential. This is sensitive to any differences in tire size amongst the 4 wheels. The clueless previous owner fitted 225/70 R15 replacement tires on the front axle whilst retaining the original 225/75 R15 on the rear. I spotted this at the time of purchase, but the local Jeep dealer and the Jeep specialist dismissed it as unimportant After about an hour on the highway a loud, but intermittent noise was heard from the transmission sounding like a failed bearing. It turned out to be the viscous coupling "winding up" and/or over-heating. The problem was rectified after having done much investigative work on axles and wheel bearings, by simply replacing the tires so they all matched.
Exhaust manifold cracked - another common problem on the I-6, heard loudest when cold, solved with $60 removal, welding up the crack and refitting.
Oil pressure sensor switch replaced because oil pressure gauge showing excessive pressure.
Visor clip broken.
Fuel filler flap catch - plastic end just broke off so the flap could not be held shut. Repaired by inserting self-tapping screw into stub.
Driver's power window switches - sometimes do not work, have to lean over to activate relevant window's control which restores driver's controls.
Centre interior light - plastic mounting clips inside fatigue fractured. Repaired with Araldite epoxy adhesive.
Tailgate mounting screws always coming loose.
Remote locking control not working - too stingy to pay $100 for new control. Power locking switches on front doors just as useful after opening car with key.
Engine mountings - both broken up. $200 replacement.
Front shock absorbers and steering damper replaced due to heavy leaking after long and very bumpy off-road trip.
Suspension bushes require replacement - I am looking for good after-market ones like polybushes. Any ideas?
The only time the car has let me down was due to the low ratio gear change being loose and getting stuck in Neutral when changing from Low to High. Fixed at the time by manipulating the lever by hand from underneath the car.