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)
Deliberate mistake: Lee's old crew of three are shooting various caliber handguns at Chloe and Lee's sister. Chloe took cover behind a kitchen island. Kitchen islands are made of thin wood, the only piping in them is plastic and some brass/copper. All of those handgun calibers would have penetrated the kitchen island. (00:45:45 - 00:47:00)
Lucifer! Lucifer! Lucifer! - S5-E2
Character mistake: Chloe and Lucifer are sitting in Chloe's police cruiser staking out a suspect's car, and they get into a pursuit with the suspect in his Porsche. Chloe's police cruiser had no police lights or sirens blaring during the pursuit. Plus they are in a heavily populated metropolis; doesn't make any sense why they wouldn't have their lights on. It's standard police procedure to alert other drivers an emergency vehicle is on route, so they can yield/pull over and take care. (00:22:20 - 00:24:00)
Plot hole: Lucifer and Amenadiel realise baby Charlie calms down and gets put to sleep when he sees Lucifer's devil face. Dan just left Amenadiel's house, and he gets a phone call with Lucifer's voice telling him to come back to the house. He turns around and sees through the window Lucifer's devil face. It is revealed that Lucifer's evil twin brother called Dan to expose Lucifer. Makes no sense how Michael knew that Charlie responds to Lucifer in that way. He would've been seen peeking through a window. (00:49:35 - 00:52:00)
Suggested correction: You essentially explained the plot. Michael had been watching them the whole time. In fact, when Michael calls Dan, Dan first responds with "hey, man, what's up?" because he saw that it was Lucifer calling him. One way for Michael to have Lucifer's phone is because he saw Lucifer throw it out the window earlier.
Plot hole: Lucifer's evil brother Michael appears too Dan as he is praying upon Charlotte's grave from heaven. He tells Dan he can right all of his wrongs. His plan is to hurt Lucifer. It's stated that God sees all and hears all. "The eyes of the Lord are everywhere, keeping watch on the wicked and the good" (Proverbs 15:3). Doesn't make sense how Michael is able to travel from the Silver City to Earth to hurt Lucifer without Dad knowing or having any input, since Michael has a direct line to his Dad. (00:17:00 - 00:19:40)
Other mistake: When Maze is knocked down by Lucifer the second time, the footage used of her on the ground is the same footage from when she got knocked down the first time.
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)
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.
A Chance At a Happy Ending - S5-E16
Other mistake: After Amenadiel's necklace pin is removed, Chloe tells lucifer to get the blade, and he picks it up with the hilt still attached. But we saw in an earlier season that without that pin to hold it all together, the hilt just falls off.
A Chance At a Happy Ending - S5-E16
Continuity mistake: A guy with a face tattoo is in the opening scene, then the tattoo isn't there when the guard gets up.
