Continuity mistake: When Anna is holding the "virtual pet" after realising it has died, in the shots from the front she is holding it in both hands, but from the back it's only in her right hand. It's tricky to see because there is a pile of papers in the way, but her left hand is folded in front of her in the shots from behind.
Continuity mistake: Peter, Elizabeth, and Romano are with the little boy who has organ reversal and as Romano says "genetic breakthroughs are in the wings", Peter puts on one glove. As Lizzie asks him if something is wrong, he is putting on the glove again. As they continue to talk, he begins to examine Rodney, but when the shot changes, he is still putting on his gloves.
Continuity mistake: In season 2, Doug mentioned that he hadn't seen or spoken to his father in 22 years, since he was twelve. But when he's going through his father's things at the motel, he finds pictures of himself from high school. Plus, he mentions his father teaching him how to drive when he was about 13 or 14.
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: Doug goes into the ER room to respond to the boy, who's saying "go away." His mother has her arm around his head and is telling the drunk with his teeth out to go away. Then the shot changes and we see the boy's head, but no mother. A quick shot change and there she is again, cradling his head.
Continuity mistake: Near the beginning of the show, Doug is examining baby Josh and puts his stethoscope in his ears. Kerry says, "Your actions are totally irresponsible", and the shot goes to Doug. There is no sign of the stethoscope anywhere. The next shot, from behind him, shows it's around his neck. He then takes it off and the next shot should show it in his hands - but it's disappeared again.