I have worked on this model many times. For this year range you should make sure that it does have an oil cooler. Some early vehicles did not come with and oil cooler. To check look in the front wheel well as the oil cooler is usually installed on the passenger side wheel sell toward the front of the tire. You can usually see it through the fins in the wheel arch cover. This helps to keep the oil temperature regulated better.
The high pressure fuel pumps have a warranty now for 10 years 120,000 miles if my memory serves me. We do not do many of these pumps any more as the new pump is much better and no longer is as prone to failure. You should ask if the vehicle has ever had a high pressure pump installed and at what mileage.
The injectors, unfortunately, are the new problem that is still quite common. They can fail and cause pressure to bleed out so you have a long crank like it is a bad high pressure fuel pump, the leaking fuel can cause the catalytic converters to fail early, and in rare cases I have seen the engine hydro-lock with fuel or the exhaust be so full of fuel it needs to be removed and drained. So I would also ask if the injectors have been replaced and at what mileage. The new injectors do not fail as often but I have seen even new injectors leak fuel and had a brand new injector cause a hydro lock. But over all the quality of the injectors is better at this time.
The other thing to look for is the waste gate rattle. BMW has increased the warranty on the turbo's to 8 years 80,000 as they tend to fail due to the pivot arm bushing wearing and causing the turbo to not seal well. So when you look at a vehicle give it a quick hard rev at idle and listen for a metallic jingle type noise as it winds down. The louder the noise the more loose the valve is and the vehicle should be avoided or new turbos installed. BMW even covers the turbos just for the noise issue at this time as long as it makes the noise after several revs in a row.
As for other issues, I have seen VANOS solenoid fail and some other minor items like radiators leaking in the bottom corners but over all the above is the main failures. The big thing to do is to look for a vehicle that actually has a big service history that repairs where done to these systems so you know newer parts are installed. Also if the vehicle has the turbo rattle it may be covered under warranty and it can be repaired before you purchase. So there are some good things due to the warranty.
I would buy this vehicle, as it is a pleasure to drive and when it is running well can bring a smile to you face. Reliability is on the low side but if it has had a lot of updated parts it makes it a bit more reliable.
One more thing to consider before buying is to have the dealer perform a carbon cleaning of the intake valves. At 70 to 80,000 miles they can be gummed up with carbon due to the direct injection system and it can starve the vehicle of power. The symptom for this is usually a bit of a skip felt when started cold at idle. It would be worth checking the vehicle you are going to purchase a few times on a cold start to make sure it does not have this or tell the dealer you will purchase as long as the intake valves are cleaned with the walnut shell blaster and you would like pictures of before and after.
I hope this information is helpful to you. I tried to add as much detail for you as I could. If you could please provide positive feedback it would be greatly appreciated. Thank you.