I too have had my fair share of Mini Drama. I purchased this car since my Mortgage lender told me I needed to build credit to buy my first house. I thought it was my lucky day when I drove onto the lot and saw a Mini Cooper. In Oct 2010 I purchased an '04 Mini Cooper (pepper white). I'm in love with her.
Although my problems haven't been as major they're still troubling.
My power steering will just randomly stop working. I was told by one mechanic I needed a new power steering pump. $2k
Another who is a huge Mini Fan tells me there's something in/on/near the powersteering area that gets clogged/dirty & causes the intermittent power steering drama.

Recently I noticed while driving over 40mph and going around a curve (to the left) there's a garbly noise coming from the back left of the car (I think). Haven't had this looked at yet.

CV Boot on the passenger side went out that was about $140 (not horrible).

Car died one day, wouldn't take a jump unless you used a super special jumper from a tow truck. It was a bad battery which BMW charged $250 for.

For the last few weeks Mini is intermittantly squeeling...not sure why or what it is but it sounds like a belt. Its almost always happening when I reverse and have the wheel tightly to the left. Or when the car first takes off in the morning

My Mini is a 5speed and I've been noticing shuddering/shaking when using gears 1-3 mostly one and two just when you're first taking off. This might be my lack of knowlege with a 5spd but it's a recent happening never happened before.

I saw your post and thought I'd share but I will post this as my own too. Just looking to see if other have experienced the same things. I live in a smaller city so other than 'BMW' there isn't really somewhere to take Mini. I'm thinking about going to the Mini Dealershop in Naperville to have it looked at.

 

$2k for the power steering is flat out nuts ...
Lifetime warranted rebuilt BBA remans are $400 , power steering fan $150 Labor and fluid was $300 is what I paid

 

The power steering randomly went out again and this time I decided to take Mini to a Mini Dealership and find out the problem. They said the pump is definitely bad. $1200 for parts & labor and the part itself is like $915. Other than serpentine belts (sp) my mini is in excellent health which I guess I'm thankful for LOL

 

Find an independent mechanic who works on Coopers. I made the mistake of going to the dealer and they grossly overcharge. I was just told that I need a new A/C compressor, and the part alone was $750. I can buy them all day long for $300 from reputable parts vendors, brand new compressor.

 

Well I'm happy and shocked to report the Power Steering problem I was orignally facing was due to this serpentine belt and pully needing replaced. Mini was making a 'sqeeking' noise in the mornings on a cold start. I assumed its got to be belt related so I took it to my local BMW (Basney BMW South Bend, IN) who orginally told me it was $230 to replace the belt. An hour later they called to tell me the pulley which goes along with the belt is now frozen and I'm looking at $560 for the total repair. I contacted an import repair guy on the other side of town who said he could fix it for $200 (belt & pully). He fixes both of my bosses imports which is how I found him. I called BMW, told them I'd be picking up the car, skipping the repair for now since the car runs fine other than the squeek. Service Mgr wasn't happy but oh well. Picked it up and not even 5 minutes off the lot I swear it sounded like Mini blew up. Apparently the belt broke bc the pully was frozen (what BMW Mgr said). I had Mini towed to the other repair shop and Mini was fixed the next day! This was about five weeks ago and Mini's been fine so far!

 

I'm glad your situation worked out.

 

The shuddering/shaking at take off is most likely worn out front control arm bushings. Probably will need the ball joint bushings replaced at the same time