Continuity mistake: When Lucifer helps Amenadiel, who has been stabbed with one of Mazikeen's daggers, Lucifer has one hand on Amenadiel and one by the dagger. The camera cuts, and now he has both hands on Amenadiel. (00:21:45)
Continuity mistake: When Linda asks Amenadiel if he is a real doctor, he has both hands raised. Camera cuts and now he only has one raised. (00:08:20)
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!