One problem related to engine burning oil has been reported for the 2006 BMW 3 Series. The most recently reported issues are listed below.
My BMW 300 series wagon (2006) had a brake and emergency warning light turn on. There was also a smell of burning oil. My mechanic identified the problem as broken aluminum bolts on the cylinder. He said he personally sees this all the time on 2006 models, that BMW is aware, and that they redesigned the part for later years. Likewise, my BMW dealer is aware of it and a simple google search finds at least 1000 complaints posted at various sites on the web. Aluminum does not hold up in this setting and these bolts cost more than$1200 to repair. I am told by my mechanic that it usually happens after 60k miles which means most are off warranty. BMW is aware and should either do a courtesy repair or be forced to do the right thing by NHTSA.