I have a 2005 S that I purchased new. It is one of the best cars I've ever owned, absolutely no problems whatsoever, and a thrill to drive.
The main thing you might look for is a warranty. If there's a factory or aftermarket warranty, this is your insurance against major problems and expense for repairs. You don't want to pay for a knackered supercharger or its peripherals, very costly. The Getrag 6 speed gearbox is also a relatively pricey item to replace.
However, unless the car has been unduly thrashed and neglected the mechanicals are essentially bulletproof. Electricals, drivetrain, braking, etc., are high quality and will last a long time if the car has been cared for properly.
Ask the owner for receipts for any major work or replaced parts. Hopefully, the owner may also have documentation of required periodic maintenance. If the factory-required maintenance from the MINI dealer(i.e., at 5k, 20K, etc.) has not been performed, beware.
Otherwise, perform a normal, pre-purchase checklist on the car. The engine should purr as smooth as silk with no hiccups even on the coldest days. The six speed gearbox is exceptionally smooth and practically shifts by itself. Regarding the suspension, expect a stiff ride, after all it is an "S" model. You should experience no wheel hop or rattles of any kind.
Overall, expect a very solid, <span style="text-decoration: underline">very</span> agile car with no anomalies. Don't settle for less.
Good luck, let us know . . .