Other mistake: Danny, while driving home with his family, hits a man with his car. Danny gets out of the car to attend to the man, but his wife, Linda, who is a nurse, does not get out of the car to render aid to the man. (00:02:18)
Continuity mistake: Frank and Henry are up late, 3am, and, talking about how his late wife Mary never wanted to see her youngest go into the Family Business. Henry says how proud Mary was in the day of Jamie's graduation. But Mary was already dead by the pilot, when Jamie graduated.
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.