Check out
www.scirocco.org, there is a great tech section which gives step by step diagnosis which includes part #'s and tools etc. I have a 16v which experiences similar problems at startup either cold or warm. I've changed the fuel filter, plugs, air filter, run Techron through twice and LubroMoly once and no significant change. I'm looking toward the injectors next. The article on scirocco.org suggests vacuum problems. I'd say its worth a look. If your mixture screw is completely missing then you should be running all out of shape. The car needs the proper mixture or all kinds of bad things can happen to the smoothness of the idle, etc. Good luck.