The tightest that I've both used successfully and measured was ~5 mils, but I would only go that low for a problematic workpiece. It's possible I've gone lower than that by now, but I haven't measured in a while as doing so is somewhat involved (I used a reflective/metallurgical microscope) and fairly pointless once you have the hang of things.
Steve Elliott has
some 'scope shots on his page showing a 4-mil setback.
Like most people, when I need a close-set cap-iron I adjust it with a bright light reflecting from the iron, and advance the cap iron until a uniform (or symmetric if the blade is rounded) sliver shows all the way across. I used to do it under a 4X magnifier with bright lightning, but realized that that was unneccessarily time-consuming. You can judge it well enough with the naked eye if you get a good specular reflection from the blade back.