No, don't adjust the screw, that's fine by your description.

You've simply got a bind somewhere in the rotating assembly or linkage (ok, cable). Usually you can fix it by simply cleaning and lubricating things. A can of carburetor cleaner and a toothbrush do wonders.

There is a chance it's being caused by some wear, and some piece needs to be replaced. You can carefully locate exactly what piece is sticking by carefully moving things with your finger when it's high idling, to locate exactly what piece is holding the throttle slightly open. It's harder to find than you'd expect.