We currently have 3 x R53 Cooper S hatchbacks in our family - an 06, an 04 and an 02. All have the smile factor when you drive - and only minor differences in road feel and trim. They are all great to drive.
Some quick tips for you:
1) Look under the car for oil leaks - especially for any on the left side of the vehicle under the gearbox (viewed from the rear looking to the front) which could indicate a leaky rear main crankshaft oil seal (that's an expensive one to fix because the gearbox, clutch and flywheel all have to come off just to replace a $10 part).
2) R53 series Power steering pumps are all typically noisy & whine like mad. Haven't had one go yet, but others report they can be prone to failure. One of ours weeps a bit of oil from the bottom of the oil tank reservoir which runs down the pipes and underneath. Not a difficult fix but a pain none the less.
3) Their 6 speed manual gearboxes are pretty strong, but watch out for a worn clutch as these too can be expensive to fix - check the friction take-up point on the clutch pedal (should be about 1/2 way down - 2/3 way down as you let up the pedal) - a friction take up that's right down on the floorboards or a heavy clutch pedal could mean its on the way out (if it's a stock clutch) OR the vehicle "might" have an after market competition clutch some of which just have a heavier pedal feel as they're meant more for race use rather than everyday road.
I don't have any experience with their auto boxes as our are all manual gearboxes - perhaps others who have an auto can comment on that.
4) We've had a few squeaks and rattles to fix - some in the dash, some in the rear suspension and a boot monkey that proved tricky to find but eventually required us to change the whole boot-lid catch mechanism to make it go away.
5) Be absolutely sure to check the colour of the engine oil - if it's thick and black then the engine's had no love recently. It should be honey in colour if its been changed. Likewise, unscrew the lid of the Brake master cylinder - it should be like light coloured honey in colour if its clean. If the brake fluid is dark brown or tending toward blackish in colour (Yuk!) then again that car's had no love from any mechanic.
6) Check the tread wear pattern on the front and rear tyres. If the tread pattern is wearing rough like a saw tooth, of scuffing on the edges then the car has been driven hard or steering/suspension is mis-aligned.
7) Open the glovebox and find the Service manual (or service receipts). Look at what has been done in the past, and how often. Look for a car with a good & regular service history.
8) One of our cars makes a kind of a moose noise when you have the steering wheel turned hard over and driving forward (eg: U-turns or tight maneuvering). We've not yet figured that one out - but suspect its got something to do with the rubber CV joint boots.
9) Listen very carefully to the engine on first start-up (engine must be cold). It shouldn't rattle or make any odd rattly noises - engine rattles can be often $$$ to fix.
10) Last tip - if you're not mechanical yourself, take someone along with you who is if you can. If you can't take someone with you, make inquiries with your local Road Service organization or mechanic to see if they will provide a professional inspection and report on the vehicle before you part with your deposit. A trained eye might cost you a few $$ to get them to look closely at the vehicle, but they should be impartial and give you good information about the mechanical condition of the car and whether its been crash-repaired etc.
In Australia, we can buy a used car inspection service from organizations such as the NRMA etc. who will give you a full inspection and car history report. Could be good insurance so you know exactly what you're getting yourself into before you give any money to the salesman. If the car yard or owner wont agree to a pre-purchase inspection - run the other way like mad as they are trying to hide something.
Good luck with your purchase, and please come back and post pictures of your vehicle for us all to admire. Happy MINI-ing!