Nightmares - S3-E7
Continuity mistake: In the very first episode Frank Reagan is getting dressed to go to Jamie's graduation ceremony. He slips on his watch and then takes a ring with a blue stone (looks sort of like a class ring) and puts it on. It is definitely and obviously a large blue stone. Then in this episode, near The End, when Frank is sitting at the bar talking to Garrett, as Frank lifts his drink in his right hand, and Garrett says "Thank you, Frank", that "class ring" has a very definite and obviously large red stone. (00:01:20 - 00:40:50)
Continuity mistake: Jamie's car is suddenly yellow when offering driving lessons. In previous episodes, the car is blue. (00:40:18 - 00:41:16)
Continuity mistake: At the start of the episode, when Frank opens/closes the refrigerator door we see the door's layout, and the door bin cover is under the top shelf compartment. As he makes himself the sandwich Erin and Nicky walk in, and when Nicky opens the fridge door it's an entirely different interior style with the door bin cover at the top.
Continuity mistake: Near the episode's end, Danny gets into a shootout with Tommy in a house. The first two shots from Danny go into the wall. The next two shots, you don't see where they go as Danny runs to a different location. On Danny's next two shots, the wall doesn't have holes, and then two holes show up. With Danny out of bullets, he attacks Tommy from behind. When they wrestle, there are four holes now in the wall.
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.