One problem related to engine burning oil has been reported for the 2006 BMW 330. The most recently reported issues are listed below.
This issue is with the piston rings of the BMW m54 engine. It burns oil at a crazy rate and only now are people finally figuring out that this is the issue. BMW lists several other fixes for the oil burning issue, but none of them solve the problem causing the owner to seek repairs that don't solve the issue. BMW states that it is "normal" for the m54 engine to burn up to 1 quart of oil for every 1000 miles. This engine is in many different BMW models and many owners are effected. My car now burns about 1 quart for every 500 miles I drive.