I have a new American Standard valve stem that is leaking from around the central shaft (in case my attached image doesn't work, see http://neilnowatzki.com/graphics/plumbing/valveStem.jpg). It leaks when the valve is partially open, but not when fully closed or fully open. No water leaks from the spout when the valve is closed. I installed new valve stems and seats on both sides, and the cold side works perfectly. Water water also leaks from the hot valve stem when the cold water is on (not sure that's relevant). On the hot side, I've tried a new stem, the old stem with washers stolen from the new stem, and another new stem, all with the same results. Completely baffled here, any ideas?

Nice visual... There is either packing seal or O-ring under this elongated nut ( where the blue droplet is coming out from ).
First try to tighten it up 1/2 turn. See if that helps. If not, you will have to unscrew. You will see either used up packing seal or O ring. Replace it. Back to you. Milo

The old stems had no O-rings, the new ones did. I went back and compared the old and new valve stems after reading about a similar issue on another web site. Turns out there are very minor differences in both the seat and stem. However, I have an all-new valve stem with an old seat (couldn't remove the old one) that work perfectly on the cold side.

So I tried this: I put the old seat back in on the hot side. Then I installed the old stem with all the old washers, except I stole a new rubber thingy off the end of a new stem and put it on the old stem (the part that seals against the valve seat). IT STILL LEAKED, just as before. Removed the stem. Extremely discouraged, decided to give up for the day. I re-installed the valve stem so that I could turn the hot water on for the rest of the house, and now IT DOESN'T LEAK. What was the issue? Still no idea. What did I do differently? Nothing as far as I can tell. If at first you don't succeed...