Continuity mistake: During the kitchen scene in the beginning, the number of pictures on the fridge keep changing in various shots. (00:03:00)
Plot hole: Lucifer's evil brother Michael appears too Dan as he is praying upon Charlotte's grave from heaven. He tells Dan he can right all of his wrongs. His plan is to hurt Lucifer. It's stated that God sees all and hears all. "The eyes of the Lord are everywhere, keeping watch on the wicked and the good" (Proverbs 15:3). Doesn't make sense how Michael is able to travel from the Silver City to Earth to hurt Lucifer without Dad knowing or having any input, since Michael has a direct line to his Dad. (00:17:00 - 00:19:40)
Sympathy for the Goddess - S2-E17
Plot hole: Charlotte tells Chloe that she was talking to the man on the phone when she hears gunshots. Being a veteran detective Chloe should have noticed since the man's gun was in his pocket (Chloe comments that his phone was found on him) that he couldn't have been using it when he was shot, therefore Charlotte was lying. Yet she never realised this.
Other mistake: If Lucifer is only vulnerable when Chloe is around, why is he bleeding when his brother is hitting him on the beach after Lucifer burnt his wings? Chloe is nowhere around, why is he bleeding?
Suggested correction: Angels can hurt other angels, this has been shown throughout the show. Amenadiel even told Remy as much (not to mention that Remy hurt Amenadiel).
Plot hole: Lucifer and Amenadiel realise baby Charlie calms down and gets put to sleep when he sees Lucifer's devil face. Dan just left Amenadiel's house, and he gets a phone call with Lucifer's voice telling him to come back to the house. He turns around and sees through the window Lucifer's devil face. It is revealed that Lucifer's evil twin brother called Dan to expose Lucifer. Makes no sense how Michael knew that Charlie responds to Lucifer in that way. He would've been seen peeking through a window. (00:49:35 - 00:52:00)
Suggested correction: You essentially explained the plot. Michael had been watching them the whole time. In fact, when Michael calls Dan, Dan first responds with "hey, man, what's up?" because he saw that it was Lucifer calling him. One way for Michael to have Lucifer's phone is because he saw Lucifer throw it out the window earlier.