This might not be coming from the oil filler cap per se, even though it probably is.
I would personally try to confirm or eliminate a leaky cap by stuffing a paper towel into the space between the cap and the flywheel cover to produce a "foot print" of where the oil is actually coming from.
The point here is that the oil mist may be coming from a different source and being blown out through the opening in the flywheel cover by the draft from the flywheel fan.
Take the cap off. Clean the tube and cap as well as you can to get rid of oil that may already be there.
Next, wrap a piece of clean paper towel around the tube, stuffing a good portion of the towel down below the hole in the flywheel cover. Fold the remainder of the paper towel out onto the top surface of the flywheel cover and reseat the cap on the tube, taking care not to allow any of the towel to get meshed into the cap "threads".
Run the engine just a few minutes and then take the cap off, but leave the paper towel in place..
If you see fresh oil visible on the paper towel where the cap itself was, then your cap is not sealing properly, perhaps a damaged, out of place, or missing o-ring or gasket may be the cause.
If the part of the towel immediately adjacent to the cap is clean, carefully remove the towel, watching for signs of oil spatter as you withdraw it. If the oil is being carried by the fan draft, the towel will show signs of oil on the towel below the flywheel cover.
It's also possible that the tube itself has a crack or fissure in it. If it appears that the cap is leaking but there are no signs of a defect in the cap, inspect the tube to see if the tube has split or cracked. I believe the tube is an injection molded plastic component. As such, it will feature a "parting line" where the mold halves fitted together during manufacture of the tube. The parting line would be my prime suspect of how a tube might fail by splitting open.

This post was edited by mownie on Mon, Jun 30, 14 at 9:27

Thanks mownie for the paper towel trick to locate a source of the leak. Well I stuffed paper towels around the fill tube as suggested and ran the engine for 5 minutes with HOOD UP, and there was no presence of oil on the paper towel...so I wondered what could be going on. I shut the hood and lifted it back up, and then there was oil on the paper towel!! I realized then that the foam filter (attached to the hood) was soaked with oil. I took the filter off, stuffed paper around the fill tube, and cut my lawn. There was no oil splash from what I could see!!!

At this point, I am assuming the maybe the fill tube dip stick was left slightly open at some stage late last year, and the foam filter absorbed the oil that sprayed out. I probably ended tightening it up after a periodic check of the oil level late last year or early spring. But the oil absorbed into the filter on the hood kept depositing oil on the engine cover, and thus falsely making me think there was a continual leak.

I am washing out the foam filter, and then will have to see if the problem re-appears or not. I hope that is all it was. I will post back if the oil re-appears after a few lawn cuttings.

Thanks mownie for the paper towel suggestion!!!

Well, I wooda never thunk about that, but glad you got pointed in the right direction after all. :^)