The newspaper photo of a grinning Les Klumpsky (David Figlioli) is a cropped still from when he was taken into the elevator. Of the people in the scene, only Ella had a camera, but she didn't use it to photograph him (and legally wouldn't have been allowed to release it to the press so soon in any case).
Right before Chloe is kidnapped, she is writing in a notebook. The position of this notebook changes positions between shots.
When Lucifer puts the snake back in the bag, he comments that "it's not even poisonous". Snakes aren't poisonous; they're venomous. A poison needs to ingested or absorbed through the skin, whereas a venom must be injected into the bloodstream to have any effect.
LilyMan85's "firsthand" accounts of Whisper Killer murders are copy-pasted excerpts from forensic studies essays on the real-life Zodiac Killer. All of the selections are written from a neutral "academic" point-of-view, rather than in first person, and detail a very different modus operandi to the Whisper Killer's. The only similarity between the two is in both being serial killers and in general physical description.
When Maze is fighting Lucifer in the police station, she lunges at him several times and it can be seen [basically when the frame is stopped], that she is not fighting Tom Ellis's Lucifer, but a stuntman, and, at one point, it looks like he is African-American. The same with Amenadiel fighting Michael, at certain points, he is obviously not fighting the real Michael.
They found the victim's house by tracking am IP address used to log into a dark web message board. It is nearly impossible to track these IP addresses if it is really a dark web site and extremely unlikely that a website like this would log user-data.
Ellas says the killer's username is "LilyMan85", but when she looks up his posts, the screen shows the name "LilyMan" with no numbers. Everyone accepts this as being the same person.
Ella, being a skilled forensic scientist, should have known right away that the dead girl in the house wasn't Chloe. They could smell the dead body from the front door and there were flies. That couldn't be possible after less than one day of death.