hi
well if you could tell me what your budget is i will gladly help you out!
just some normal stuff, look out for rust!!! the mini is one of the most prone to rust ever so be careful ie: if the car looks like its sunk in the middle, walk away, if the rust is not bad then you can easily repair it, so dont be detured by a little brown stuff but keep in mind that it might not look rusty but sometimes theres something lerking beneath the nice shiny paint, hence the use of a poking screwdriver to find any unsightly holes
i could tell u about mechanicals but i need to know your budget!!! i work in a mini shop so i know a bit of rust when i see it!!! and i can give u the lo down on some of the mech gremlins to look for 
cheers
when it breaks down a lot...... 