Well, if it's a wood door just sand it a bit and then clean any dirt, mildew, dust off with warm water and repaint. No need for a pressure washer.
Oops, mis-read the post......an outdoor shed it is! Yes you can gently pressure wash an outdoor shed. No need for much more than 1600 psi to clean off all the gunk. Keep a stiff brush and some warm water with Krud Kutter in it for stubborn spots.