Other mistake: In the scene immediately after the opening credits, Jim is talking to Melinda on the phone. Right as he's hanging up, someone calls out "Dr. Clancy? Got a minute?", to which Jim waves in acknowledgement and starts up the stairs. (Jim's spirit has been in Sam Lucas' body since season 4 and in an earlier season 5 episode, his white coat is embroidered S. James Lucas, M.D).
Other mistake: The captain talks about the "outflow valve", which has a distinctive rectangular shape and is fitted flush with an opening in the aircraft skin. It would be immediately recognizable by any crew member because it part of the walkaround inspection before each flight. He is holding a round pneumatic supply valve instead, which is part of the internal ductwork.