I am painting a front grill which is a real pain since the base coat had to be applied from so many angles to get full coverage.  Now I applying the clearcoat over the black base coat.  Each time a spray the clear coat there is some over spray on the part after it dry the overspray turns to dust.

Then the next time a try to add more the clearcoat and have to clean the grill again to try and remove all the dust which slicks pretty well to the part.  So I use a damp rag to wipe it off, then a dry one, then a have to hand wipe the fuzz off.

Why is this dust coming from?  It there some wrong?  Is there anything I can do?

Blue Energy

What are you using to spray with? If you are using a spray can, it sounds like it's too hot and the clear is drying before it has a chance to adhere properly.

If you are using your own equipment, it sounds like you did not add enough thinner.

I am using a spray can.  I tried reduce the temp to below 70 and now it seams to be working better.  At least there is no more dust.  The clear cost go on with glossy spots and dull areas.  Is this normal?  I sanded the glossy area down a little with 1200 and then resprayed, but they keeps coming back.

The clearcoat will not shine without rubbing compound as it will just dry flat. Use a medium grade rubbing compound and the clearcoat will shine right up.