Fog of War - S10-E14
Factual error: During the funeral towards The End of the episode, both Jamie and Eddie are wearing white shirts with their dress uniforms. In the NYPD, only Lieutenant and above wear white shirts, like the show has portrayed. The color doesn't change for the dress uniform. (00:38:35 - 00:41:14)
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.