One problem related to engine burning oil has been reported for the 2003 BMW 325. The most recently reported issues are listed below.
The oil filter housing gasket fails on BMW cars. It is a mesh gasket between the engine and the block where the oil enters/exits the filter. The repair is about $600 and fails frequently on these cars. It causes oil to leak onto the block and gives a strong burning oil smell. Oil can accumulate on top of the engine depending on the severity of the leak. Oil blows and covers the oil filter housing and the inside of the hood with a spray of sticky oil.