Things to look at are stripped gears in the sunroof motor (they were cheap plastic), dash warping from sun/heat, dry/cracking interior trim plastic (radio trim, brake light cover, center seatbelt cover etc...), shifter cable endlinks that are worn (loose shifter feeling) and of course look for the typical stuff (leaking fluids, coolant/oil mixing, IMRC end links not attached, abnormal tire wear). Depending on condition, $3000 seems to get you a pretty good one.
They suffer the typical problems a 15 year old car will have (paint fade, worn interior, worn parts).
Mine has been pretty good for what it is. I found it collecting dust in a back dealer lot. I did a new alt/battery when I got it and had to replace the rack/pinion. It's been a good runner. I put over 100 miles a day on it running highway and city traffic. It has over 160,000 on the clock.
Do some reading on Contour.org for opinions on them. Some of the little SVT specific parts are hard to find, but the hard core guys usually have a solution. The 2.5L motor was widely used, so those parts aren't too bad to get at your local store. There are some 'fun' upgrades if you want to spend some money. The 3.0L swap is very popular. There are brake upgrades from Wilwood or even use PRT's kit (http://www.prtautosport.com) that adapts the Mustang's 13" brakes to the front. There are some various suspension upgrades you can pick through as well from places like BAT (http://www.batinc.net/contour.htm).