I experience the same accelerated oil usage with my old 240D. The only explanation I can come up with, is that the oil gets a little sheared and is quicker to make it past all the areas where you don't want it to pass. Any comments from anyone else about this would also satisfy my curiosity.
On the M103 engine, it is common to see a leak at the bottom of upper timing cover at the front of the engine. There is a seal at the bottom of this half round looking cover that commonly has a slight leak. I've been keeping an eye on mine for about 80,000 miles. It wets the front passenger side of the engine just a little, but doesn't drop anything on the shop floor. When it starts leaking bad enough to leak on the floor, I'll pay it some attention. Unless it's leaking enough to stain the floor, I'd wash the engine and then keep a close eye on it. If it is a bad leak, wash the engine to determine for sure where the leak is coming from, and then fix it as soon as you can.
'84 Euro 240D, 516K miles
'88 300E 5 Speed
Over 800,000 miles in