Picked up a brand new 3cfm harbor freight vacuum pump at and auction here in town for 30 bucks, looking for something like this(its the yellow and black filter sitting vert) Its called a oil mist eliminator...
We use a similar product where I work, and may even have a couple of the Eliminators the originals got replaced with. While I can't go into many details on our processes, we have ovens where we heat up a printed film over a product and it gets vacuumed down and an ink sublimation process transfers the design onto the product. While the process is fairly clean, it makes some smoke and other undesirables and some get sucked into the vacuum. The oil mist separator catches it before it reaches the pump. I believe we empty the container a couple times a week. No idea what the OP would needed it for, but if he is vacuuming with anything that has a liquid in it, it would be needed.
To the OP I am unaware of anything else that could be used, maybe a moisture filter for compressed air? Wouldn't hurt to try I guess, very similar basic concept.
Just like your air compressor or engine, Vacuum pumps are oil lubricated. Some of that oil can carry over into the exhaust of the unit so it is common to filter the air blowing out of the vacuum pump to remove oil and other contaminates. On the process side of the pump you filter the inlet of the pump to remove contaminates before they are sucked into the pump head.
Look up Edwards vacuum - you want a "KF" flange mist trap - it's a box with both mist element and carbon odor element stacked. A foreline trap is put inline to protect the pump.
I built one of these pumps for veneer, a little more complex because I wanted to use parts I had around and buy as little as possible. I added a few features too.
Some vacuum pumps (like the ones used in HVAC work) use oil. Some do not use oil and will fail if you put oil in, so be careful.