Dirty Skin

Try wiping down the top inside of smoker, also clean out the top vent hole with bottle brush.

You don't say what smoker, but GQUE is correct. After a period of not being used, the layer of grease/fat built up on the inside top of the smoker flakes off and can drop on the food the next smoke. I find this happens more in the winter. I also wipe down the top surface with a damp rag just to remove the flakes of grease that will discolor the next product. Definitely not a health issue, but not appetizing.

I have an 08 (steel/stainless steel small model) that does the same thing.
I clean the top of the inside every time, put a paper towel on a rack in the top slot to help block drips.

I even changed out the top vent fitting with one from a Smokin-It smoker. That fitting has a bigger diameter hole, is much thinner so it is almost flush with the sheetmetal.  My theory is the original fitting was cooling  the smoke down and allowing condensation to form and drip.  I have less now. 

Next thing I'm going to try is to change the insulation on top portion to a fiberglass mat material used for engine exhaust insulation (1/2 thick and you can hold you hand on it when used to insulate headers on a diesel engine).

I have exactly the same effect on the inside of the lid of my gas grill, which does not have a vent hole.

If cooking say a whole chicken or turkey... after it reaches the "color" you want, wrap it in butter soaked cheesecloth.  Smoke will still get through but skin won't be as "sooty."  Also after it's finished you can throw it in a hot oven to "crisp" up the skin.  All in all smoked poultry skin is not great... unless you are cooking butter pan chicken thighs... 

Nordy