Continuity mistake: Romano is standing outside an ER room watching through the glass. To his left, down the hall, we can see a woman pushing someone in a wheelchair. But when the shot goes to him entering the room, there's an extra behind him on the left pushing a large cart of supplies - there was nowhere for him to come from.
Continuity mistake: Lizzie sees Dr. Morgenstern for the first time in the ER and she asks Kerry, "Who the hell was that?", and Kerry answers, "Our Chief of Emergency Medicine." Yet when he resigns in Episode 19, he tells Peter he's resigning as Chief of Surgery. Unless he held both positions, Kerry's answer could not be considered a character mistake, as she would have known what his position was.
Continuity mistake: Near the beginning of the show, Peter is feeding Reese in the hospital cafeteria. Reese has a bowl of pablum that is in the middle of his high chair tray. The next shot shows the bowl way over to the left, even though there was no time for the change in position.