Had a strange thing happen to me today. I was selling stuff at Primm; one Single Shotgun that most definitely existed in my inventory would not appear on the list of items I could sell when talking to the shopkeeper. Tried dropping it and picking it up, tried equipping and un-equipping- nothing worked. What's up with that?

That's probably a consequence of you having stolen this particular weapon while it was considered property of a Primm resident. This works exactly the same for all stolen items in the game. To verify this, try selling it at a different trader (Goodsprings, for instance).

I didn't steal it. Picked it up off a powder ganger's corpse. Can't test it in Goodsprings because I dropped it on the ground in Vicky and Vance in frustration, and now picking it up is "stealing".