Trivia: There is a Blue Bloods and Sopranos connection through the actors and creators. The Sopranos' actors who played bad guys or had connections to the mob mostly played cops or good guys on Blue Bloods.
Trivia: Although Len Cariou plays Tom Selleck's father, he's only five years older than Selleck.
Trivia: In episode 10x7 "Higher Standards" the last scene with Frank and Jaime was filmed at one of the four piers (specifically, it's the northern pier at 48th Ave) which are part of Gantry Plaza State Park, at Long Island City in Queens. Directly across the East River is the United Nations Headquarters in Manhattan.
Trivia: In episode 7x4 "Mob Rules" the last scene was filmed at Brooklyn's Kent Street Pier, part of Transmitter Park in Greenpoint. When Frank shows up, the large "Jeffrey Gamblero" graffiti can be seen in the background near the India Street Pier (which people miss as a Ferry stop). The graffiti has since been painted over.
Trivia: In episode 2x22 "Mother's Day" the scene at the start was filmed at Brooklyn's American Veterans Memorial Pier, at Bay Ridge Ave aka 69th St, in Bay Ridge (off Belt Pkwy). The location and design of this pier is distinctive and also sentimental (particularly to older Brooklynites).
Trivia: In episode 2x1 "Mercy" the last scene was filmed at Brooklyn's Valentino Pier (it's also known as Coffey Street Pier) in Red Hook. It had been renamed for a Brooklyn firefighter who heroically died in the line of duty, and the area's full name is Louis Valentino Jr Park and Pier. It's an appreciated green area in the middle of a lot of buildings. Bit of trivia to add, Valentino Pier is featured in a short video with Rosie Perez.
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.