Continuity mistake: During the kitchen scene in the beginning, the number of pictures on the fridge keep changing in various shots. (00:03:00)
Continuity mistake: At the start when Trixie comes running in to give Lucifer a hug, Lucifer has got a jar in his hand. As the shot changes to him actually being hugged, the jar simply vanishes from his hand. (00:03:05)
Continuity mistake: At the end of the kitchen scene, Dan turns to tell Chloe he is disappointed in her. When he does this, in the shot from behind Chloe looking at Dan, Chloe has her hand on the door frame at head height and is leaning against her hand. When the shot changes to behind Dan looking at Chloe her hand and head have moved instantly with no time to do so. (00:04:00)
Continuity mistake: When Chloe is kicking Lucifer out of the kitchen at the start she has her hands on her hips in one shot and down by her sides in the next. When Lucifer finally admits defeat and says "Fine" (00:04:00)
Visible crew/equipment: When Chloe shuts the door on Dan, a stage light is reflected in the glass of the door. (00:04:10)
Continuity mistake: When Lucifer tells Carver that "This woman [Chloe] won't have sex with me!" Chloe's reaction changes from the close to long shots. Note her mouth. (00:14:50)
Continuity mistake: When Lucifer is walking towards the cowering Lindsay, she has her gun in her left hand. When the shot changes to behind Lucifer, the gun is now gone. (00:34:20)
Other mistake: When Lucifer and Chloe are talking about the Player after-party, the same extra walks by twice (in the same direction without having enough time to double back). After Lucifer says "sex afterward" and it cuts back to Chloe the women is seen and then when Chloe walks away.
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!