The vet tech leaves the dog on the tall table and leaves the room. NO vet tech, or ANYONE who takes care of animals, would EVER lead a dog up on a table like that. It could fall or jump off and break its legs or back.
When Dean reads the note to Castiel by the truck, the written note says "I see you standing by the truck.." Dean says, "I see you standing alone by the truck.." This is a big mistake, as Dean being alone is the key to the Gorgon not being able to see Castiel or angels in general.