Nick,
Oil can be burned, leaked, or vented...
[1] Leaks...
I believe the tubes that OR75 is referring to are the oil return lines from the valves back to the oil pan.
It is a good observation, many a drip can originate from these small hose clamps. Another drip source is the quick change oil valve at the bottom of the oil pan. These can get old and drip too. Old valve covers leak through their old style cork seals. Evenly tightening these old screws can stop the leaks. Have your mechanic update cork seals for the new silicone style.
Take a good look at the back of the engine where the magnetos and oil screens are. Serious oil leaks can be found here...
Some cases leak between halves.
These are all accesible through the side panels or removing the top of the cowling. Oil leaks usually will leave a tell tale mess inside the cowling. I am pretty sure the floor of the cowl should be clean unless oil is dripping in there.
Q: Is it clean inside the cowl?
[2] Burned
I concur with Piloto on how to determine if the oil is burned by inspecting the exhaust residue in the pipes. If oil is exiting through the cylinders, it will show up in the exhaust pipes and on spark plugs.
Q: Is oily black material showing in the exhaust pipe?
[3] Vented
Is there a way to measure how much gets vented without investing in expensive recovery equipment? I saw an experimental with a plastic bottle at the end of the case vent. (I don't believe this would work for a Mooney). Vented oil leaves by the vent tube that has it's end overboard. Vented oil does not appear anywhere inside the cowling.
When checking for proper venting. The vent tube should have a small hole near the engine. This allows venting in the event the vent tube gets blocked (by ice).
[4] Observations
I found that long climbs at high power pushed alot of oil overboard in my O360. 1 qt every 5 hours, and it seemed like alot for an engine with 1,200 hrs SMOH.
Best regards,
-a-