The main area of concern is the carbon build up in the intake, which is a result of recirculating exhaust gases back into the engine (which is not running as hot as it is should, due to people babying it or shorter drives), for better emissions. The build up takes about 50k miles to accumulate and affect the engine. The cleanup cost is about $1500 or so. My 335d had that done under CPO warranty at about 50k miles (previous owner), which was on my list of things to look out for.
The harmonic balancer, also seems to go on these engines, which is a DIY for a capable DIYourselfer, and perhaps a $600 or so repair at an indy shop.
Other than these, there are occasional other issues that come up here and there, but not across the board. If OP lives outside of California, there are many modifications that can be done to the engine to avoid the build up and other potential emission induced issues altogether.
I had a 2011 535i 6spd manual that I loved, and sold at about 36k miles. Beautiful engine, beautiful car. During that ownership, I was given a 535d as a loaner for a week while dealership was doing some work on the 535i. That loaner made me promise myself that my next BMW will be the 35d variety.
Given the fantastic experience I had with the 2007 328i E90 that my wife owned, one of the best handling sedans in my opinion, I looked for and found a clean unmolested 2011 E90 335d (last model year they came in E90) with about 55k miles on it years later and bought it on the spot.
35d engine is extremely rewarding and combined with the handling of E70 X5, is a great combo in an SUV, or with the E90 body it makes one of the best real world sport sedan experiences.
