Lady Parts - S2-E4
Continuity mistake: Chloe has a bruise on her left eyebrow and a cut on her right after the fight in the bar, but when she grabs Lucifer's phone the cut and bruise have swapped sides on her face, and then when she storms off they go back to their original sides. (00:30:48 - 00:31:30)

Lady Parts - S2-E4
Continuity mistake: In the tiki bar, when Chloe says she's LAPD, Maze chokes on her drink and her bottle is by her shoulder. When the shot changes to a close-up of Maze, the bottle is now up by her mouth. (00:17:30)
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!