Things to look for when shopping:
1) 2002 and early 2003 models came with the 45RFE transmission out of the Dodge Ram [good for towing]
2) Same year time frame also gets you: Slightly taller springs (3/4"), 18 gallon gas tank, different power-steering profile and rear drum brakes that function as a killer parking brake.
3) Some early run 2003's and all KJ's after April 2003 came with 42RLE transmission which does the job... Those vehicles also get rear disk brakes, 19 gallon tank and shorter springs.
4) 2005+ MY's have a known window regulator problem resulting in failures. There is a fix now, but it costs you money at the dealership. 2005-2006 MY Liberty’s are most affected by this.
5) The rear body seam behind the flipper glass, on the back of the KJ, is rust starts forming. Also check the door seams on the rear doors. Poor drainage at the rear door area makes it a common area for rust. Make sure you look at both areas so you know what shape the body is in.
6) Renegade models came with a 160A alternator. Regular trucks came with 132A alternator. 132A is enough, but just FYI on the bigger alternator. The vehicle computer controls voltage so no swapping in bigger alternators for more juice.
7) Select-Trac TC allows for fulltime 4x4 driving, but is a weaker TC than the standard Command-Trac unit that most have.

Make sure the LBJ recall has been preformed. Surely it has but just in case, run the VIN number through the Jeep.com website to make sure.
9) The speed sensor plugs into the top of the diff and the parking brake cable can rub / fray through the speed sensor wire. If you see intermittent speedometer operation - chances are the wire needs repair.
10) The multifunction stalk (turn signal side) can cause the dash lights to flicker. Not a huge issue but you can wiggle the stalk and look for this. Replacing the stalk fixes the issue.
11) Make sure the HVAC blower works on all 4 settings. The resistor block fails in these about every 2 or 3 years with constant use. The resistor block is an easy fix that costs about 17 dollars and takes less than 15 minutes.
12) Valve spring failure is randomly reported on the 3.7L engine after 100K miles of use. It’s a random issue that isn't widespread - but does exist so it's worth knowing about.
13) Tow limit for KJ with Manual Trans = 3500 pounds. Tow limit for KJ with Auto Trans and tow package [factory rated] = 5000 pounds. [3500 w/o Tow package according to the factory]
I'd find a nice 2002. They are the best (biased opinion) because they get the stronger transmission, have an extra power-outlet in the front center stack and don't exhibit many problems. Look for one with a mechanical engine fan under the hood... That's a sure fire way to tell you it has the tow package. The tow package comes with a 7-pin trailer harness properly wired by the factory.
The KJ is not prewired for trailer brakes but you can add one if you need it [depending on your tow weight]
I tow all over the place with my sailboat and love the KJ as a tow vehicle.