Continuity mistake: Near The End of the episode Frank Reagan pulls up to the house of the woman who has been scamming New Yorkers with the fake 911 charity. Immediately before he arrives she is putting suitcases in the trunk of her car. As he pulls up the suitcases in the trunk are different.
Plot hole: Someone entered Erin and Nicky's apartment, moved furniture, and disturbed photos. In the morning, Nicky is leaving the apartment to go to school, and she just opens the door without unlocking any of the locks or removing the door chain. It's NYC, and their apartment door isn't secured during the night or day, and ADA Erin Reagan doesn't think to question why the door is unlocked. (00:00:37)
Answer: It's a common cop show plot device. If the police on the show always acted in the most logical way (i.e. not alerting a suspect to their presence) the show wouldn't have the opportunity for an exciting foot chase.