In Tick, Tick, Tick, the killer clearly fired bullets indicating the name "Nikki." In Boom!, there is a scene in the killer's home with the name "Nicky" etched into a mirror. Timestamp 17.08. Spelling is inconsistent.
The infamous tropes Enhance Button, Facial Recognition Software and Magical Database all appear. First, the surveillance camera footage where the criminal appears gets all three tropes applied. The FBI Enhance Button zooms in on his face and brings out more detail, whereas in real world only pixelated mush would appear, because you can't create information out of nothing. Then, the Facial Recognition Software calculates what his face would look like from a different angle; again creating information out of nothing. Finally, the Magical Database finds a 100% reliable match in about 10 seconds. Later, there is some vague mush seen on the background of the FBI agent's kidnap video and Enhance Button again creates information out of nothing by enlarging the blots to what can clearly be identified as a landmark bridge.
In Season 1 (Home is Where the Heart Stops), Castle and Beckett are at the shooting range, and he gets three shots in the 10-ring with ease; however, in this episode of Castle when he is aiming the gun at Dunn, he shoots him in the hand, but then says to Kate "I was aiming for his head." While Castle is shown to be an excellent pistol shot on the range, he is not a trained police officer or a skilled/experienced fighter. Therefore, it's entirely plausible that having to shoot under stress would severely affect his marksmanship. This happens even to trained police officers and soldiers.
A painted advertisement on a wall for the Palace Newsreel Theater is visible at one point. The Palace Newsreel Theater is a Los Angeles movie theater.