The Would-Be Prince of Darkness - S1-E3
Plot hole: During the credits, Chloe said of the victim "coroner puts her time of death between 1 and 3am", and she does indeed ask Ty's obsessive fan / ex-gf where has she been during that timeframe. When she looks at the security tape, the timecode starts rolling at 22:18 and goes on "for 3 hours." That does not account for the time of the murder at all, she has no alibi for the second half of the suspected timeframe! Not to mention, she said she saw Ty kiss the victim. When could she possibly have seen that? It's unlikely that before 10pm Ty was already drunk and getting randy with the girl, with the house full of guests. (00:25:00)
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)
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)
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.
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").
Character mistake: When trying to decipher what the letters from the dermal implants spell, Lucifer rearranges the letters and says "Hilii Fircus, it means 'children of the goat.'" However, the correct phrase was Filii Hircus, not Hilii Fircus. (00:13:27)
Factual error: When we see Dan's computer while he's running the trace there are 4 results shown, but they're all the same: 256.256.256.256, an impossible IP address.
Character mistake: Chloe, Maze, and Ellen are discussing a murder and the death of Vernon Gill who was killed when hit by a car after he was fleeing pursuit from Chloe and Maze. They were discussing Dirty Doug who came in last night and Maze says "he came in last night and Gill said he threatened him for taking credit for Lee's murder." How could Gill say anything when he was already dead from being hit by a car. Should be "he said Gill threatened him" not Gill said since Gill's dead, in hell. (00:30:55 - 00:32:00)
They're Back, Aren't They? - S3-E1
Audio problem: When the cops draw their Glocks, they make a cocking sound. Glocks are striker fired, there are no safeties or hammers on the exterior to manually operate for the handgun to make a noise. (00:03:20)
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)
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)
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: The quantity of blood on the door changes between shots, incoherently, when Jimmy is hurting himself, smashing his head on it. (00:42:35)
Audio problem: Lucifer is playing the piano at Lux, but he steps away from the piano about a second before the piano stops playing. (00:04:06)
The Would-Be Prince of Darkness - S1-E3
Continuity mistake: Lucifer gets waken up after his very PG foursome by Ty. When he says "Can you just help me, please?" Lucifer does not have his right hand on the shoulder of the girl, in contrast with the earlier and following take. (00:06:15)
Plot hole: There is a rather confusing revelation when Chloe is shown the recording Joe Fields made for his daughter to see in the event that he were to die. In the recording, Fields tells his daughter that he did not kill the cop (Chloe's father). Chloe then notices that this is true because based on the timestamp on a sign in the background of the recording, he made the video 3 minutes before her father was killed. But this would be impossible because at that point the cop in question was still alive.
Suggested correction: That was the whole point of the episode. Joe Fields never killed Chloe's dad (officer Decker). Fields was innocent and took the fall for his murder. The time on the sign showed that Fields was too far away to have killed her dad. Her dad was in fact assassinated (arranged by Perry Smith) and not killed in a robbery attempt as previously believed.
But why would he even make a tape saying he didn't kill the cop if it hadn't even happened yet? Makes no sense. Did he go back in time?
I think you should rewatch the episode. He already agreed to take the fall for the murder. He knew the murder was going to happen. He made the tape for his daughter before he went to prison (and possibly made it before the murder as to further prove his innocent). The tape was to be given to his daughter after he died so that it wouldn't affect the deal he made.
They never made the connection that he knew the murder was going to happen, instead they went on a wild goose chase instead of going bit by bit.
But then as Bishop is saying, Joe Fields knew that the hit was going to go down. He made the video declaring his innocence so his daughter would eventually get the tape. Whether he knew that he would be exonerated is another matter. But the point remains the same. He knew that the cop was going to be killed and simply prepared for it. No mistake.
Continuity mistake: When Maze says goodbye to Lucifer and takes off on her motorcycle, the cars around change. You can see 2 cars parked with a car next to it with its blinker on. Then there are 3 parked cars and the end one has its hatchback up. Then as she drives off, it's a van. In the next shot the van and hatchback are gone.
Is This Really How It's Going To End?! - S5-E15
Continuity mistake: When Dan hands Ella the phone number, he's holding it by pinching it on the bottom. In the next shot, he's holding it on the side.
Who's da New King of Hell? - S4-E10
Continuity mistake: When Lucifer, as the Devil, tells the demons to go home, all the bodies fall down. We see the bodies fall down behind Chloe, too. After the shot of the Devil, the camera goes back to Chloe and the bodies all fall down again.