Who's da New King of Hell? - S4-E10
Continuity mistake: When Lucifer, as the Devil, tells the demons to go home, all the bodies fall down. We see the bodies fall down behind Chloe, too. After the shot of the Devil, the camera goes back to Chloe and the bodies all fall down again.
Expire Erect - S4-E5
Continuity mistake: Near the end, as Dan says "this is all on me", in a shot from behind her Maze is spinning her knife then stops, gripping it pointing downwards in her fist. Cut to a new angle and her hand is instantly turned over, with the knife sticking out sideways.
Other mistake: When Julian is in custody, being interviewed by Chloe, a lawyer comes in and says a judge has released Julian on his own recognizance. Then Chloe asks what happened to the $2M bail and the lawyer says it's already been paid in full. It's one or the other, if he was released on his own recognizance, no bail would have to be paid. If the bail has been paid, he would be released and no need for a judge's order. Not to mention the fact that all of this takes place the same day he's brought to the station and hasn't had a bail hearing. He didn't even seem to have been processed, he was just being questioned.
Devil Is as Devil Does - S4-E7
Character mistake: On Earl D. Bolden Jr.'s wanted poster, it says "if you see this man NO NOT approach..." It should say "DO NOT."
Answer: At least as far as clothing goes, I was in regular clothes when my wife gave birth, only changing into scrubs when they thought we'd have to move to an operating room (but ended up not needing to), otherwise I'd just have stayed in them. The room was also pretty much a regular hospital room, but no doubt there were some birth-specific differences I wasn't aware of!