One of my lever set watches has a strange problem. When the lever is pulled out, the watch sets correctly forward and back. When the lever is pushed back in, the watch will wind when the crown is turned clockwise but if the crown is turned the other way the hands move backwards. What could be causing this?

Sounds like your clutch is hanging up. Maybe a chipped leaf or an engagement problem. I would pull the clutch out and clean it all up and look for burrs or chipped/bent leafs. I have an Illinois that's doing the same thing right now.

Someone else said something about a spring. Whatever it is, I can't do it myself. I'd have to send it out. I stay away from anything that requires any disassembly past taking a movement out of a case and putting one in.