Other mistake: Throughout the episode, Lucifer's car has a California license plate - but that is, just one. He is missing the one in the front. In the following episode the car does have the regular 2 plates, and when he is pulled over at the beginning (and keeps being around cops all the time), nobody raises an eyebrow at the violation of the code.
Lucifer, Stay. Good Devil. - S1-E2
Other mistake: We are shown several times the first person perspective of a paparazzi camera, with the HUD. From a diegetic point of view though, it is used in a way that lacks coherence. For instance, in the red carpet scene the photo count goes down by one every time the shutter clicks, while in the car scene it does not go down at all. And it really could not have been Josh's camera in the red carpet scene, because it photographed Chloe once he already escaped and from behind.
Other mistake: When Lucifer and Chloe are talking about the Player after-party, the same extra walks by twice (in the same direction without having enough time to double back). After Lucifer says "sex afterward" and it cuts back to Chloe the women is seen and then when Chloe walks away.
Lucifer, Stay. Good Devil. - S1-E2
Other mistake: The dynamic of the scene with the paparazzi outside the party is quite absurd: forgetting the fact that the paparazzo just happened to have amazing parking privileges (the only sedan in the street, allowed somehow right by the red carpet!) the timing is all wrong, as he "just" made his escape a minute later, witnessed by Chloe walking away just then from the paparazzi brawl. She had walked past their lot already over 30 seconds before, while Lucifer stayed behind forcing the comical confession out of 'Friar Tuck'. (00:26:00 - 00:26:35)
Lucifer, Stay. Good Devil. - S1-E2
Other mistake: Despite the presence of multiple paparazzi on site while a civilian opens a police car, drags the main murder suspect out of it for some rough questioning and generally creates a suspicious scene, nothing about it leaks in the news (one guy even takes picture of the other side of the road!).
Answer: As Cain theorises in a later episode, it's Chloe's love, not presence. This early on, Chloe had no strong feelings for Lucifer, so had no effect on his immortality. In fact even more recently he's back to being invulnerable around her after speculation that he chose to let himself be vulnerable. So while there's a degree of flexibility / retconning going on, it's all explained in-show.
Jon Sandys ★