My GF daily drives a 2002 3.0 auto AWD Escape. I'm not familiar with the 4 cylinder/manual versions, but for the sake of the "Learn Me" I'll throw in some insight on the rest of the car.
The major theme with these, or at least the one I deal with, is corrosion. And not just the rot that's prevalent in the rockers and rear quarters/shock towers, but things that corrode and either fall off the car or cause other larger parts to fall off or almost fall off the car, like:
-The hinges for the rear hatch glass. I don't drive the car that often, and I always forget to look at which handle I squeeze to open the hatch. I accidentally hit the one for the glass once and when I went to shut it, one of the hinges failed and I almost had a heart attack thinking I needed to catch it before it hit the ground. It was a challenge to get it to shut again, but it held enough to allow the car to be drive-able, albeit with some rain coming in, while I waited for some readily available replacements from Dorman to come in.
-Rear shock shaft snapped off at the tower due to rust. The lower bolts that have 60% of a hex head and some tacked on retainer weren't fun to remove.
-Gas tank strap rusted and broke off, causing the tank to rest on top of the driveshaft. There's a one step above tin foil "shield" that covers the bottom of the tank that basically disintegrates as well.
-The original exhausts flex section rotted out and eventually broke causing the exhaust to hang down in the front. I bought $500 worth of replacement peices for RockAuto, but couldn't do it my self because the original Y-pipe nuts/studs are nearly impossible to deal with without a lift. Cost another $200 to have a muffler shop address that. $700 later, and the replacement system didn't even make it 3 years before the flex section started leaking again and then the tail broke off a couple month ago. It currently has the muffler hanging about 2 inches above the ground... I really don't want to spend that money on it again...
Others:
-Seems pretty common for Ford radios of that era to go haywire at some point. The one in my GF's had some buttons do some weird stuff, and the volume knob would forget which way was up or down and the you'd go to turn it down just a hair and would increase the volume full blast.
-Headlight harnesses like to melt eventually
-Somewhere between the MC and reservoir went bad and leaked all of the brake fluid out causing the brakes to get soft
-Rubber on front brake lines eventually breaks down and leaks
-The tiny screws/bolts that hold up the cover under the engine rust out and break, so you have to get creative with some zipties
If you change your mind on the 3.0/Auto, or someone else stumbles on this thread:
-The 3.0's love to leak oil from the timing chain cover, and it's apparently a difficult job without removing the engine. It leaks on the exhaust, which smells wonderful when stopped at a light. I just top it off every few weeks.
-The auto shift linkage bushings can come apart and leave the car stranded. I McGyvered a new bushing out of a vacuum cap at the bottom of tool box when stranded once, and haven't touched it since. That was over 3 years ago.
-The coils and some emissions related parts like to fail, but are easy to fix
-IMO, the alternator job sucks, but isn't as bad as advertised
-Transmissions seem to be a common failure point, but I've never had an issue
All that said, I'd still take it over the vehicle it replaced, which was a 2008 4x4/Auto/4cyl Jeep Patriot. The Escape has way nicer interior and visibility, is much more pleasant to drive (with a V6, not sure about the 4cyl), and (still with the V6) gets better gas mileage.
Ironically, if you're looking for a cheap AWD 4 Cylinder AND manual vehicle in the ilk of the Escape/Tribute/VUE/etc., the Patriot/Compass did offer such a combo. But beware, they are AWFUL.