TBH, all turbo, DI engines, regardless of manufacturer, are going to be a bit high-strung, in terms of reliability. If you start to dissect the all of the various engines that fit in that catagory, you'll find issues.
That being said, my best friend bought a 2007 E90 335i with 75k miles, and it's now about to hit 90k with no issues under his watch. According to the service history, it had the HPFP, injectors, and battery replaced at port, back in late 2006 and that's about it...
I picked up my 2010 135i as a 12,000 mile old, CPO car this February, and now at 23,000, it's yet to have any notable issues, and it's service history noted nothing out of the ordinary. They did to replace my rear lights when I bought it? Apparently that's a 1-series thing. The lights weren't broken, but they did it just to say it had been taken care of.
TLDR: All cars can have problems. All cars can not have problems.