Character mistake: When Doug leaves work, he tells Carol he is Going Home to watch the channel 11 Yule log. Later on, he shows up at her house with Charlie and Carol says, "I thought you were watching the channel 9 Yule log." It's possibly a slip of the tongue from Carol, but most likely it would be ingrained in their heads which local channel features a Yule log at Christmas.
Character mistake: When Dr. Keaton rushes back into the OR to take over from Peter, she moves forward, pushing the door open with her hands. No surgeon would EVER enter an OR this way-it would contaminate her hands. The proper way is to back into the room, keeping one's hands in the air and free.