Bit like asking how long a piece of string is-the longer you own it and the more miles you do the more likely things will go wrong! Alternator 100k miles and maybe water pump=think timing chains 130k ish, radiator maybe around this point, battery-say every 6 years depending on quality-shocks will be tired at 100k too! Rule of thumb from past experience only!!! and of course if you look after it well and are lucky-electrics etc are an unknown. Wear and tear items excluded eg brakes-discs/pads!
I do understand if you keep car long enough, things might/will break. I have heard few stories from my local colleagues and friends who owned German car which were BMW and Audi. Many of them reported that their cars were pretty much trouble free(minor stuff only) for the first 60 to 70K and then things started to go out one by one. So most of them got rid of their vehicles by 80 to 90K as it wouldn't be financially good thing to keep fixing stuff.
Quick summary of few of my previous vehicles:
-Owned 1995 Corolla which I bought in 2000 (bought it from auction which had been in a collision with another vehicle). It has 50K on it when I bough it. Kept it only for 3 years as I wanted something better. I did have to repair starter once, so no big deal and my local mechanic did it.
-Bought pretty much new 2004 Corolla S, kept it for 3 years, so no issues at all. Just wanted something a bit faster and nicer.
-Had 2003 Acura TL loaded which I too bough used in 2006 which had around 70K on it(highway miles). Kept it for 3 years and sold when car had 96K on it. I had to replace front brakes and rotors. Also Acura had couple of recalls performed which were free.
-Bought new Toyota/Scion xD in 2008 and modded it a bit throughout its life. Kept it for around 8 years and sold it when it had 56K miles. 1 recall was performed and 1 time early in the first 3 years water pump was leaking, so Toyota replaced under warranty.
This is my first MINI and first used German car and I do appreciate this little and yet fun to drive car

, I just don't want major issues early in its life which could indicate the build quality issues.
I bought it with less than 20K miles and within the year I drove about 5K, which is not much. No track or driving hard from the stop light. Only occasional fun on the twisty roads and highways

With that said, the MINI did the following in my 1 year of ownership:
-Replaced lower control arms. When I came to the dealer with this issue, the service advisor told me that he "believes "these were already replaced on the vehicle a year or so ago. Possible when another owner had it. Don't know for sure if lower control arms were replaced once or twice.
-Front upper strut mount made some rubber-rubbing noise, so dealer replaced struts and upper mounts.
-The recent issue was with clunk/thump noise in the back...tech replaced rear shock but though it didn't help and put back my original shocks but for the sake of diagnosis tightened the center nut on the shock rod. Which did make the noise go away. Don't know if it was temp or permanent fix.
All these things were covered under warranty and if this car won't have major issues in the next 5 years, I would keep it.