Jed knows Chloe married Dan, but doesn't know she's a cop. In the show's continuity, Chloe married Dan after she became a cop. It makes no sense that Jed would know the former, but not the latter, when the latter occurred first.
Ella said that the conditions with the headphones were ideal to maximize the voltage that killed DL Matt Pexxa. Those conditions decreased electrical resistance and increased conductivity, thereby maximizing the current (which is the flow of electrons), not the voltage (which is the force that is pushing the electrons).
Chloe calls Lucifer to relay a question meant for Jed. It's unclear why she wouldn't just call Jed. However she may have simply wanted to talk to Lucifer.
The explosion throws dirt and debris over an area that extends past Chloe and Lucifer without any of it landing on them. Lucifer reflexively brushes off his sleeve, but it was already clean.
Chloe mounts an expensive, large-scale sting at Lux but only has herself, Ella, Linda, and Maze searching for the murder suspect instead of a crew of undercover officers with safety training or powers of arrest. Chloe assumes by the suspect's screen name that they are female and limits the search to women, although, as a detective, she would have had experience both with usernames that have nothing to do with a person's everyday appearance and with people taking over the accounts of legitimate people in order to pretend to be them. The search is divided into quadrants each person searches only once, without accounting for the possibility that individuals and groups at a dance party move around. A lot of time and effort could have been saved by having undercover officers disguised as Lux's bouncers to check guests at the door before they even got inside.
Much is made of Jed's alibi for Pexxa's murder, but he doesn't have one. All he says is that he was with his producer for some period, which doesn't account for either the headphones being sabotaged (which could have been cone anytime) or the time of the murder when Jed was waiting to go on stage after Pexxa.