First of all, thanks a million for the suggestions and sympathy about the paint problem on my front door.
I took the paint back to Lowe's, where the high school age kid behind the counter listened to my tale with a vacant expression and said, "Huh. That's weird." Long silence. I suggested "we" call Valspar. She rummaged around, found a number and handed it to me. I left. I know a lost cause when I see one.
I called the number for Valspar and reached a real live person on the first ring at 6:30 in the evening. He spoke English. He knew about paint. How cool is that?
I described the problem, and he explained what happened. Bottom line: I'm screwed.
On the paint can it says, among other things, to paint only when the surface and air temperatures are 50 to 90 degrees. I knew that. That's why we took the door down and painted it in the nice, heated wood shop out back.
What the can did not say was that it has to stay at that temperature for at least 24 hours. We hung it back up the same day and let it freeze overnight. Paint Guy didn't really explain why that causes the chalking, but he did say it is going to keep right on doing that no matter how often I wipe it off.
The solution is to sand it down and repaint it, and to let it cure at the proper temperature. He recommended waiting for spring.