At 32:56 when Lucifer goes to turn a corner, there's a car in the street he's turning into. A few seconds later when they cut to the next shot of him entering the street there is no sign of the car in the street or that it was ever there in the first place.
When Linda is discussing Lucifer's names, she brings up "Samael" which she implies means "light bringer". Samael actually means "God's poison" meaning he's the one that deals out God's punishments. The name "Lucifer" is the name that means "light bringer".
The body is found in Long Beach. Long Beach and Los Angeles are separate cities and the Los Angeles Police Department would not investigate a crime in Long Beach.
At around 7:25 into the episode, when Lucifer is playing with the flashlight, the shot cuts to him over the corpse for about 5 seconds. The security guards 'corpse' can clearly be seen breathing in this shot, as the stomach rises and falls.
Dan and Trixie improvise an outfit for him out of Chloe's clothes that fits perfectly, even though Chloe is three inches shorter and of much slighter build than him.
At 17:48- a real therapist would be extremely concerned if her clients' CONFIDENTIAL sessions could be overheard by others.