Continuity mistake: At the beginning of the episode, a cop pulls Lucifer over. The car stops with the front wheels on white road markings. When Lucifer is shown taking off again, the street is just not the same, there's no white horizontal lines, and a manhole appears under the car. (00:02:45)
Continuity mistake: When Lucifer talks to the killer in agony in the car wreck, blood streaks change on his face between shots (in particular, he has blood coming from the corner of his moith in the last shot, from the side, but he had none a moment before, in close-ups). (00:09:40)
Continuity mistake: Lucifer walks down the stairs into 2 Vile's mansion; first person he comes across is carrying a glass, wearing a black T-shirt and grey undershirt sticking out. The guy is walking towards Lucifer as if he were going to use the stairs Lucifer is descending, but just vanishes in the following shot, only to reappear at the next cut, taking the stairs as it seemed bound to happen all along. (00:16:15)
Continuity mistake: During the scene in the school corridor with Lucifer sitting down and talking to Chloe's daughter, the same extras keep doing erratic back-and-forth for no reason (for instance the girl with a white jacket and pink shoulder bag) or just plain wrong (the kid with the horizontal striped maroon sweater who walks twice past Lucifer early in the convo). (00:24:50 - 00:25:50)
Factual error: The record producer is holding a pistol model 1911 or 1911A1 which is a .45 caliber handgun with a standard magazine capacity of 7 +1 rounds, the +1 being loaded in the chamber, however newer magazines hold 8 +1. Therefore, this handgun can hold a maximum of 9 rounds, however the producer fires 10 shots before Lucifer grabs him. Newer 1911 style pistols are now produced in 9mm which have a greater capacity but the pistol held by the producer was a standard 45 ACP judging by the metal and finish. (00:37:38 - 00:39:18)
Other mistake: Throughout the episode, Lucifer's car has a California license plate - but that is, just one. He is missing the one in the front. In the following episode the car does have the regular 2 plates, and when he is pulled over at the beginning (and keeps being around cops all the time), nobody raises an eyebrow at the violation of the code.
Lucifer, Stay. Good Devil. - S1-E2
Continuity mistake: At the beginning, the preacher is walking around with the donation mug. The first kid to put a few bucks in does it across two shots and has a very notable yellow hand-held device when he puts the money in that was not there in the first shot. (00:02:00)
Lucifer, Stay. Good Devil. - S1-E2
Continuity mistake: When Lucifer shows his devil face to the preacher at the start, the mascot behind Lucifer changes between shots. (00:03:00)
Lucifer, Stay. Good Devil. - S1-E2
Continuity mistake: The fake preacher runs away leaving all the money behind: in the overhead shot Lucifer says "I'm here till, well, the end of times actually" turning around past a guy (big hair, big sideburns, black and blue shirt) that he already passed in the shot before as he thanked the crowd. (00:03:20)
Lucifer, Stay. Good Devil. - S1-E2
Continuity mistake: Chloe is being debriefed by her ex about the crime scene. There's a close-up of the photographer who will be the key of the case, being physically pushed away by a policeman. The scene goes on with him in the background in many shots, all on his own, snapping away as if nothing happened. (00:08:55)
Lucifer, Stay. Good Devil. - S1-E2
Continuity mistake: Lucifer easily walks past the police tape and approaches Chloe and Dan. The same paparazzis appear behind him (mostly past the police car) and behind them, opposite ends of the road. (00:09:00)
Lucifer, Stay. Good Devil. - S1-E2
Factual error: The apple scene (as it often happens with Amenadiel's scenes) does not make much sense: ignoring the fact that the liquid in the glass suffers no slowdown (we can assume that being in Lucifer's hand somehow protects it), the apple is already on its descending arc when the two are talking by the piano, but is still up there well after a minute. By the speed it moves, it should already have fallen. Also, why would it drop vertically and not continue its trajectory? (00:13:50 - 00:15:50)
Lucifer, Stay. Good Devil. - S1-E2
Continuity mistake: Lucifer tosses the ninja chemist doll towards the door, and it lands on the rug in front of it. Nobody picks up the doll, but when Chloe shoves him off the premises, the doll has disappeared. (00:17:00 - 00:18:10)
Lucifer, Stay. Good Devil. - S1-E2
Continuity mistake: Immediately after the close-up on the poster of Demon Town with Penelope Decker, Lucifer holds the trophy. From behind it's evident that Chloe's healthy arm is down her side, but in the reverse shot she has her arms crossed. (00:17:30)
Lucifer, Stay. Good Devil. - S1-E2
Continuity mistake: In the interrogation room with Nick, more than once (for instance when Lucifer says at the beginning "I don't want to know about the case") when Jeremy Davies lifts his open hands and holds them up, they are held up at a different height between one shot and the reverse. (00:18:50)
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!