Air Venturi 4500 compressor SMOKE???

I'd call AV. Smoke is never a good sign but not always a BAD sign. I see a little around one fitting ( it looks like oil). From there or elsewhere, it doesn't take much to make oil smoke. But then again, I can't tell from your pic where the smoke is coming from. 

I have a Hatsan lighting, which I think is the same type of base compressor. It does the same thing. I've been running it for over a year, and no problems. Some others may chime in, but I'm think that this is normal for these type of compressors. 

The cylindrical cap Has two vent holes on the top and the smoke is come from there.

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The smoke is probably a fine mist of oil blown out from the crank case.

When the compressor is running, air is repetitively sucked into the crank case and blown out via the breather tube. It's normal to have some oil mist carried along with the air flow. My Yong Heng has a rubber membrane inside the crankcase to minimize the amount of oil mist blown out in such manner and I have never seen any smoke coming out from the breather tube when the compressor is running. 

If the smoke you saw is produced in such way, it should have been seen right from the start instead of after 15 minutes of running. I tend to believe that air is leaking from the cylinders into crank case because of such reasons as bad piston rings. There has also been a report on such phenomenon caused by cracked piston top. At the beginning, the pressure inside the cylinder is low so the leakage is relatively slow. After running for a while and the pressure gets higher, more air is leaked into the crank case so more oil mist is blown out forming the smoke you saw.

If it does not affect the fill time significantly, you can probably leave it like that but the compressor should be used outside as the smoke is obviously bad for health.