The newer shape bmw mini's are dirt cheap , ok they look fugly but decent enough for a runabout but why are they so cheap
Only guess is reliability 
Early ones have a chrysler engine which is shit and the reworked gearbox from a Rover 25 which also wears prematurely(it was ok in the Rover),06 on goes Peugeot mechanicals which are better
I am a BINI fan, and ours has a SEPTEMBER 2001 Build sticker so it's pretty early.
The Chrysler engine has a power characteristic like the old metro turbo. Nothing below 4,000, but it loves to rev. The One only has 95 bhp, but both can be reprogrammed to have 125 bhp. I've never heard anything bad in terms of reliability of them.
Legend has it that the gearbox decision was against BMW wishes, and should have saved £150 per car, except many of them failed under warranty, despite an engineering led improvement project.
Now to me, that's not premature wear, it's poor manufacturing. We changed the oil on ours at 84K and there was a lot of debris on the magnetic drain plug. Seems to be fine though. Recon boxes are not that expensive - it's just labour costs that will kill it.
Also the electric power steering issues, can be resolved at a fraction of the cost when almost new.
If i remember correctly early metro turbos destroyed gearboxes under warranty due to midrange torque and face lift models had less midrange and more in with a bang at higher revs.
Hence my comment that the BINI cooper is the spiritual successor to the Metro Turbo.
Our BINI had to have new front wish bones and top mounts
Our 1988 mayfair, had to have all new ball joints, and new front knuckle joints.
My Old metro turbo had to have all new ball joints and new rear knuckle joints