
Continuity mistake: When Lucifer is walking towards the cowering Lindsay, she has her gun in her left hand. When the shot changes to behind Lucifer, the gun is now gone. (00:34:20)

Continuity mistake: At the start when Trixie comes running in to give Lucifer a hug, Lucifer has got a jar in his hand. As the shot changes to him actually being hugged, the jar simply vanishes from his hand. (00:03:05)

Visible crew/equipment: When Chloe shuts the door on Dan, a stage light is reflected in the glass of the door. (00:04:10)
Other mistake: When Lucifer and Chloe are talking about the Player after-party, the same extra walks by twice (in the same direction without having enough time to double back). After Lucifer says "sex afterward" and it cuts back to Chloe the women is seen and then when Chloe walks away.

Continuity mistake: When Lucifer tells Carver that "This woman [Chloe] won't have sex with me!" Chloe's reaction changes from the close to long shots. Note her mouth. (00:14:50)

Continuity mistake: At the end of the kitchen scene, Dan turns to tell Chloe he is disappointed in her. When he does this, in the shot from behind Chloe looking at Dan, Chloe has her hand on the door frame at head height and is leaning against her hand. When the shot changes to behind Dan looking at Chloe her hand and head have moved instantly with no time to do so. (00:04:00)

Continuity mistake: When Chloe is kicking Lucifer out of the kitchen at the start she has her hands on her hips in one shot and down by her sides in the next. When Lucifer finally admits defeat and says "Fine" (00:04:00)

Continuity mistake: During the kitchen scene in the beginning, the number of pictures on the fridge keep changing in various shots. (00:03:00)
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 ★