In one shot, Lucifer is reading from the book Freshman Year. In the next shot, he puts the book Sophomore Year down on the desk.
When Chloe and Lucifer are talking with the victim's publisher, at 7:47 the other actor's mark can be seen in Chloe's sunglasses.
Chloe shoots at machinery in a business to distract Lucifer from his tunnel vision. Using her service weapon for this purpose is considerably out of character for her. Also, as a member of the police force, she would be required to account for every bullet she fires, and to plausibly explain why she discharged her weapon at a piece of private property---resulting in the destruction of that property---when it was not itself a source of danger. In the logical world, neither "my partner was getting carried away" nor "I needed to get someone's attention" would pass muster. She would at the very least be faced with suspension or a psychological review, or both.