What Would Lucifer Do? - S3-E4
Other mistake: When Lucifer grabs Amenidiel's phone and is supposedly typing on it, he's holding it upside down. (00:06:25)
The Angel of San Bernardino - S3-E20
Other mistake: Lucifer's obsession with Bones is highlighted here when he confronts someone as a killer only to realise it's because he's an actor who played a killer in the Bones episode Intern in the Incinerator (a role Scott Rinker did play in real life). Kevin Alejandro (Dan) and Aimee Garcia (Ella) also played roles in Bones, which Lucifer never comments on. In fact so did Jeremiah Birkett (Lee Garner, "Mr. Said Out Bitch").
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!