The Would-Be Prince of Darkness - S1-E3
Plot hole: Lucifer is not wearing a wire, since the 'fixer' could get suspicious. In the next scene, Dan, who is the person that Lucifer should introduce, is in constant contact with Chloe for no urgent reason. Why would the fixer not check him for a wire too?
Lucifer, Stay. Good Devil. - S1-E2
Other mistake: The dynamic of the scene with the paparazzi outside the party is quite absurd: forgetting the fact that the paparazzo just happened to have amazing parking privileges (the only sedan in the street, allowed somehow right by the red carpet!) the timing is all wrong, as he "just" made his escape a minute later, witnessed by Chloe walking away just then from the paparazzi brawl. She had walked past their lot already over 30 seconds before, while Lucifer stayed behind forcing the comical confession out of 'Friar Tuck'. (00:26:00 - 00:26:35)
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
Other mistake: Despite the presence of multiple paparazzi on site while a civilian opens a police car, drags the main murder suspect out of it for some rough questioning and generally creates a suspicious scene, nothing about it leaks in the news (one guy even takes picture of the other side of the road!).
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)
The Would-Be Prince of Darkness - S1-E3
Continuity mistake: Lucifer enters the conference room of the "rebranding" of Ty. You can see Ty turn around in his chair, but after the cut he is still leaning against the table, performing the turn again a second later. (00:35:30)
The Would-Be Prince of Darkness - S1-E3
Continuity mistake: At the end of the episode, the therapist in the first part of the conversation (before she gets her heels) holds her right hand on her bosom in the close-ups, while it is lowered in the wider angle. (00:40:10)
The Would-Be Prince of Darkness - S1-E3
Continuity mistake: Joe rubs his protege Ty's shoulders saying "But we kept it out of the press." Ty has his hand raised, while in the shot before he had it on the desk. (00:35:15)
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
Revealing mistake: When Jimmy grabs the cell's door, in the shot that happens before he starts banging his head on it, the supposedly secure door gives way effortlessly, showing big gaps. (00:42:30)
Continuity mistake: At the very start of the episode, the strawberry that the woman bites into changes shape several times between shots. (00:01:30)
Revealing mistake: When Lucifer convinces Ricky not to jump off the building, it is blatantly obvious that the two actors are on a green screen and not an actual rooftop. The green glow around their heads is visible. (00:13:10)
Continuity mistake: During the kitchen scene in the beginning, the number of pictures on the fridge keep changing in various shots. (00:03:00)