Thanks, Juan, I think I see what you mean. I suspect in my case the problem had something to do with the layer used for snapping, although I never did figure out what it was. I deleted the features used for snapping, made a new feature set for that, and tried editing again, and did not get the error message (exiting the program and restarting may have helped too).
Seems like I get arbitrary errors with 10.1 that I didn't get with ArcGIS 10.0, and sometimes just shutting down and starting up again gets around the error. Not very elegant. Anyway I like your suggestion about projection and will watch out for that. Thank you.