I am finding these using the AMC258 Google method. I will paste what I find.
UPDATE: I've condensed this topic, and I've removed irrelevant posts.
Any further good suggestions will get amalgamated to this post.
Outer:
Rear hatch hinges and gasket, remote hatch release if equipped.
Rotted front "frame" rails. Rotten battery tray;
rust on undercarriage.
doors may sag(hinge pins).
Engine bay and drivetrain:
check oil color/smell and trans fluid.
amc stuff-leaky valve cover (a given).
Other engine/trans leaks.
Make sure 4wd works.
Check the condition of the boots on the CV joints. If they are torn, you may be replaceing the shafts soon.
Check operation of heater valve (the in-line one under the hood); radiator for signs of leaking, seepiing or fixed with stop leak; and the fan clutch are a few more.
Road Test (driving) and the rest:
runs rough/stalls when comming to a hard stop-clogged idle jet,vaccume leaks*****.
tires, brakes, lights, turn signals, all switches, locks windows, door levers.
sagging rear leaf springs/worn out shocks f/r.
and dont forget the mystery dent or the set of mandatory vice grips to get the hood open.
good luck.
Fan clutch extension: fan blades will turn somewhat freely when engine (and thus fan clutch) is cold. After test drive or 10-15 minutes of warmup the fan clutch should be warm or hot and should then be more difficult to turn, depending on how hot but any change is a good sign that it isn't completely shot.
Also while fiddling with fan, try to wiggle it in all directions perpendicular to the shaft direction and see if there is any movement, this is a check for the water pump bearings, if it is anything but tight then the water pump likely should be replaced soon (before it breaks).
While test driving weave left to right left and right at a reasonable speed (25-35 MPH or so) and listen for any rumbles from the front, this can be a sign of worn wheel hub bearings. Drive a few complete circles in a parking lot or similar with wheels turned to full lock and listen again for any rumble or repetative speed-relative popping and such, this is a test for the CV joints on the front axle halfshafts. Any other popping during the above swerve and hard circle tests could mean it needs ball joints.
Take a vacuum gauge along and hook it up (without creating a leak of course) to a manifold vacuum port (tee near firewall on top of intake manifold is the usual spot I use, I unplug the hose that goes to the distributor advance via the coolant temperature switch on the side of the intake manifold just in front of the carb (thing with 5 ports on it, a row of three and a row of two). Then watch the needle as it idles, it should hang out rather steady around 17 in-Hg, anything less than 15 is not good and can mean a simple carb tuning problem or sticky valves (usually the carb though). Then raise and hold RPMs as steady as possible at somewhat mid-range (unless you have a tachometer handy or the dash has one, then it'd be around 1600 RPM) and again check the vacuum gauge to ensure it is above 15. It will spike higher when you first hit the accelerator and drop to near zero for a moment when you let off again which is why you need to hold a stable RPM range while checking. Aside from vacuum leaks and such this test will help predict if the transfer case mode selector will have enough vacuum to work, by spec they require at least 15 in-Hg of vacuum. Much lower than that especially on a partially worn out transfer case shift actuator and it won't have enough pull or push to properly change modes. A lack of vacuum or a "nervous" needle that flips more than a few markings to either side of center reading can be a sign of bad valvetrain including worn out cam or worn out lifters.
Some of this is difficult to do prior to purchase, so sometimes I pull into a parking lot and quickly do all the odd vacuum gauge tests and such so the seller doesn't get annoyed or feel like you're being too picky or whatever.
Def check that 4x4 but on the later eagles its not as common a problem as the early ones. With the power windows...if one of them goes up slower than the rest you might wanna ask if you can check under the door panel (or just assume either that motor or cable is about shot)... I think someone on the fourm had to pay like $75 for a new cable. Door handle springs also go on our cars... they are $10 a shot from DC. If the car still has a working trunk area pully covering thing (yeah... you'll know what i'm talking about if it has it) that is a huge plus (from a collecting point of view). I suppose if you make a big deal about any of the things on my list its just being a nit pick... put you can look for them and mention them... as psyc ammo for price conversations
Eagle buyers out there, you better be able to read wiring and vacuum diagrams and at least be able to bake a cake . . . not that baking has anything to do with Eagles . . its more about being able to follow a recipe(instructions) . . and repair it yerself, because there are very VERY few mechanics who know anything about how to work on a car that doesn't diagnose itself.
Do not avoid buying a '86 model just because of the transfer case. It can be easily swapped to the NP129 (or other) case.