Stay away from 02's because not only do they suffer from all the same flaws as the rest of the 3rd gens, but they have their own issues like cracked/cracking rear springs, and bad 4x4 control modules. I would stay away from 4.0's for 2 reasons. 1) They get the same fuel economy, but have less HP and less Torque. 2) As state above, the chain guides are made of plastic and are notorious for failing.
As far as other issues, the transmission is the big one. Make sure to test drive it, and make sure there is no delay, stutter, or hesitation when the transmission shifts, ESPECIALLY when shifting from 2nd into 3rd.
In 2004 Ford switched to throttle by wire. My mom has an 04 Aviator, and I previously owned an 03 and I don't notice any difference. Some people complain of input lag, but I've put probably a solid 10K miles on my mom's Throttle By Wire Aviator and haven't noticed any lag.
In 2005 Ford made the Message Center, and AdvanceTrac standard on all models/trims. I've never drove, or owned a vehicle with AdvanceTrac, so I cannot comment on the merits of having this system versus not, but I've never been in a situation in any of my 2nd or 3rd gens where I would've really benefited from having it. Also in 2005 Ford introduced electronic lumbar support to the driver's seat, and redesigned the back of the center console, moving the cup holders from the fold away tray at the bottom, to molded cup holders on the top of the console, right behind the storage lid, and moved the rear vents down a few inches. I personally am not a fan of this redesign because I know my clumsy elbows would knock into drinks in the cup holders, and then I'd wind up screaming out curse words for spilling stuff on my carpet.
I just took delivery of my second 2003 Mountaineer AWD 4.6L yesterday, if that makes you feel any better. Loved my first one that I had from 08-09, and fell in love all over again with the one I just got.