I think a lot depends on the kind of Contour/Mystique thats been owned.
I currently own a bone stock 99 SVT Contour (V6 5 speed of course) with 112K miles. Im the second owner and it hasnt given me any problems. The owner before me did have to replace the antenna but generally thats not a common problem.
Ive also owned a 1996 Ford Contour SE with a V6 and 5 speed. Great car. Never had any major problems with it. Had to replace the waterpump at 70K. It later got a 3.0L swap and a turbo kit. As expected, reliability goes down to any car with extreme modifications. I sold it earlier this year.
Now, if you own an automatic transmission, youre chances of having problems is a lot greater than that of a 5 speed.
If you want peoples opinions youre probably better posting this on contour.org since it has eleventy billion more contour owners than this site. Actually, a thread about common problems and "what currently is wrong with your car" thread gets posted at least once a month on contour.org.
We also have a common reliability/issues thread in the NEW MEMBERS CLASSROOM section on contour.org thats pinned at the top since this is a common question.
http://www.contour.org/ceg-vb/showthread.php?t=39
__________________
"The CEG Nazi"
www.contour.org
1996 Ford Contour SE - Sold
3.0L V6 and Arizona Dyno Chip Turbo Kit
364 whp, 410 wtq @ 16 psi and only 4,700 rpms.
1999 Tropic Green SVT Contour - Bone stock and MINT