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 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)
Deceptive Little Parasite - S2-E15
Continuity mistake: When Chloe and Mazikeen are at the private school checking out the other parents, Chloe is alternately holding Mazikeen's hand and not holding it between shots.
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.
Liar, Liar, Slutty Dress on Fire - S2-E2
Revealing mistake: When the cops find the body in the hotel room, the actor playing the body is visibly breathing when he's supposed to be dead.
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").
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)
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.
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)
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)
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)

Quintessential Deckerstar - S3-E23
Continuity mistake: When Espinosa opens the waffle maker, initially he's holding it facing up, slightly away from him, then the shot cuts and he's holding it close to his body, facing outwards. (00:21:20)
Stewardess Interruptus - S2-E11
Continuity mistake: When Chloe tells Lucifer that her main priority is the case and that nothing is going to happen between them, her hair on the right side of her face tucks itself behind her right ear between shots. It then falls down again, then tucks itself once more.
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)
Answer: Boo Normal and Once Upon a Time were going to be part of season 4, then the show got cancelled (before being picked up elsewhere). As such they were added on to the end of season three as "bonus" episodes, hence the continuity being off. But not really a mistake, just a quirk of broadcasting. Boo Normal was originally going to be between the episodes "High School Poppycock" and "Infernal Guinea Pig" in season 3 before being slated for season 4, presumably because aside from the point you've raised, it was fairly flexible, continuity-wise.
Jon Sandys