Briefly echoing what others have said - throttle actuators will fail at some point if they are the OEM items. A company called Rebuild do refurbished ones with better parts inside and you get a lifetime warranty on them (yet to hear of a Rebuild TA failure!). Cost for this is £600 fitted whenever you are in the country IIRC. Think it's £450 if you DIY it.
E93 specific - make sure the filter just in front of the rear tyres has been cleaned as they fill up with water and kill the battery/electronics. If you see rust around the battery compartment - chances are, this has happened:
EDC, for me, was a must. The EDC software in the non comp pack models is different to the comp pack models - namely the "Sport" setting. In the non CP models, Sport is very firm and only for use on track. In the CP models, Sport is *much* better for the road, and excellent on track too.
iDrive - 2009 seemed to be the cross over year for this. Mine's a July 2009 and got the CIC. You'll just have to check each one as you look at it (the controller or double DVD drive is the giveaway). If you got a Sept 2010 model, you got bluetooth streaming courtesy of Combox. I had mine retrofitted for about £350 all in by a guy on the forum. Works great.
DCT - Buy a DCT model. DCT boxes are again almost completely problem free. The sump pan gasket can weep oil, but again, this isn't major. New revised sump pan+gasket is about £120 from BMW, but the 9 litres of oil is price at £25 per litre. It's about a £500-600 job. Apart from that, they work well, are a bit moody at lower town speeds, but anything over 10mph, they work perfectly.
Suspension - these cars are absolutely solid underneath. The suspension wears so well. EDC shocks are very expensive to buy new - but i haven't heard of a failure of them yet as they are very robust and well built. A far cry away from the E46 suspension which needed changing every 60k miles.
Engine - Largely problem free apart from the TA. Rod bearings is a big one and is a massive gamble. I decided to get mine done and boy was I glad I did - they were absolutely shot to bits and had I not got them done when I did, the engine would have lunched itself leaving me without a car for weeks and a £6000+ bill. Unfortunately, there appears to be no rhyme or reason for when they go, but it stands to reason the more owners/miles/old the car is, the more these are going to be an issue. Unfortunately, it appears that the standard thing for everyone to do when they are in charge of a V8 car is to start it up, then rev the **** out of it whilst chuckling to themselves and their mates. I imagine this happens a lot when they get traded in or when it goes to garages for services...
Tyres - Pretty expensive, but it's an M3, so expect around £800-900 for a set of Michelin Pilot Sport 4S tyres.
Brakes - Not too expensive anymore...or maybe I've just been conditioned to think they aren't. Think they are about £350 for a pair of front ATE or Genuine BMW discs. Rears are about the same.