One trick I picked up is to check the floorpans. Lift the carpet in the front footwells and give them a good prodding. Also check the inner sills (the bit running parallel with the bottom of the door on the inside of the car - check this again with the carpet lifted) and the outer sills all the way round from the bottom of the door to where it turns under the car.
Also give the inside of wheel cavities a good prod where the water sprays up from the wheel: the front bulkhead panel for the front wheels, and the seat-back panel for the rear-wheels.
Do check the state of the rear subframe as Sparky said. Although not the end of the world, it is a big job if you want to do it yourself.
Also avoid one that looks like it's been tarted up too much - it's likely to have been ragged and is now on its way out. And *do* pay attention to the oil light. Don't take any bobbins about 'oh, it's just the sensor'...
And finally (phew), listen to what your gut says. If you smell a rat, walk away - don't be tempted into taking it out of desperation.
Have fun!! I really wish I could get another Mini
Oh, and I agree with Sparky about Dave B's comments
