jaws

On my road bike I have the lateral wobble down to about 1 mm (+-). Being a type A personality, I would like to have it running dead nuts true. What is an acceptable or correct tolerance?

Retro Grouch 

It depends to a degree on the quality of the compnents that you're working with. Your hub, for example has to have a little bit of bearing clearance or it won't turn. That's going to translate into a litle bit of wobble at the rim. Lower end hubs and rims will never make a wheel that is as true as can be done with the good stuff.

For practical purposes using upper end components, I quit trying when I get wheel wobble under a millimeter. Some guys say they get down to half a millimeter, but I don't think that I'm quite that good. Eventually you will come to a point where you seem to be chasing a wobble around. When I find that point, I declare the wheel trueing process finished.

Michel Gagnon

I don't like vertical deviations because it means I'll get a bump at each tire revolution. OTOH, I don't care about horizontal deviations, as long as the wheel doesn't drag on the brakes.