I guess being a "new MINI" owner, I assumed the thread was about the new car...
'02 was not the best year for the MINI... plenty of little teething issues that go along with early production cars. Some general points:
The early Coopers (02-04) had a Midlands transmission that is prone to self destruct. Some have been ok, others... not so much. Check/ask if it has been replaced under warranty. The later cars had a Getrag 5 spd which seems to be more reliable. Avoid the CVT automatic at all costs.
The strut tower "mushrooming" is a common problem for all '02-06' coupes and '05-'08 'verts. Unless it's so bad there's actually metal tearing, it's usually fixed by pulling the strut, pounding the metal flat again, straightening (or replacing) the strut mount and reassembling with an aftermarket tower reinforcement plate on (adding camber plates also helps). Mushrooming can be visually checked by looking at the orientation of the three strut mount bolts/nuts. They should be all parallel and not "splayed" out at all.
Like other BMW's the MINI does not tolerate non-spec coolant. Can turn the insides into a goopy mess. Check the coolant reservoir - if you see "green" either run away or talk the price down a lot.
The car will probably need LCA bushings...
Earlier cars are prone to interior rattles, later cars less so, but they're still not "tight" cars. If a quiet interior is important to you, don't buy a MINI.
Tons more info here:
www.motoringfile.com
www.northamericanmotoring.com