Re: USS Copernicus, NCC-640 or 623?
Well, we never actually see the registry written anywhere (and it probably wasn't). Riker says the E is preceded by a "dash", just as is standard for those ships that actually had their miniatures labeled.
You mean this?
RIKER: It's a Federation ship. NCC one three zero five dash E. It's the Yamato, our sister ship.
Did they originally show the ship with NCC-1305-E and a later DVD version changed it to 71807?
I just watched the scene again and you're correct. Riker does indeed say "dash E." However, I'm pretty sure all scenes with the Yamato were just stock footage of the Enterprise, so the model wasn't actually labeled 1305-E.
I never make mistrakes.