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)
The Would-Be Prince of Darkness - S1-E3
Plot hole: Lucifer is not wearing a wire, since the 'fixer' could get suspicious. In the next scene, Dan, who is the person that Lucifer should introduce, is in constant contact with Chloe for no urgent reason. Why would the fixer not check him for a wire too?