Character mistake: Officer Rachel Witten tells Eddie the gun she has belonged to her dad when he was on The Job. In episode 15 of season 8 Gormley tells Frank that Witten's dad was a FDNY Battalion Chief and her uncles were police officers. In episode 12 of season 9 Officer Witten's dad Sgt. Scott Witten speaks to Frank about being on The Job. It's unlikely and not normal for someone to become a firefighter after being a police officer or vice versa or do both jobs.
Continuity mistake: Jenko and Witten confront a guy creating a commotion in a market. The felon runs past them out to the sidewalk where, somehow, the two cops are waiting and grab him.
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.