The position of Chloe's handkerchief changes between shots.
Detective Decker puts the ear bud in her right ear yet when talking to Lucifer she acts as though it's in her left.
When Detective Decker pulls her firearm (a semi-automatic) on the killer, there is the sound of a hammer being drawn back as on a revolver. There would not be a sound for the semi-auto unless she had to chamber a round which she did not do.
Chloe picks up the murder weapon with her bare hand exactly where the killer would, likely completely destroying the killers fingerprints. No cop would do this.