Continuity mistake: After the accident, Baez has a scar on her left cheek. However, during the raid, the scar moves to her right cheek and back to her left cheek. (00:27:12 - 00:49:32)
Continuity mistake: In the first two shots of the family dinner Henry is holding his fork up in his left hand, but in the third shot from behind him (facing the family) his raised left hand is empty with his fork lying across the plate, then it's back up in his hand in the fourth shot. (00:21:10)
Continuity mistake: During the family dinner, while everyone discusses the use of body cameras Frank is wearing his eyeglasses, but in the shots facing Linda during the conversation Frank's eyeglasses are gone. (00:21:40)
Continuity mistake: Henry sets down the pencil he was using on the crossword. In the next shot, as he is picking up his glass, it is in between his fingers. It shows him taking it from his hand with the other, but again in the next shot, is back on the crossword. (00:40:30)
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.
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.