After Shaw tells Beckett to go home, Kate touches her hair with a gloved right hand. The angle changes, and her right hand is now bare and she's holding the glove in her left hand.
When Castle goes to open the door to get the paper, we see that Castle did not release the chain nor unlock the door before opening it.
When the female murder victim is found on the carousel, her eyes are open and rolled up, and her mouth is slightly open. In the next scene, when Lainey is examining the body, the victim's eyes and lips are closed.
When Castle arrives at Beckett's apartment with a bottle of wine, he pours the wine and announces it to be a Chateauneuf du Pape. A Chateauneuf is a red rhone (which is packaged in a burgundy bottle). However, the wine Castle pours is from a Bordeaux bottle.
At approximately 37 minutes, Special Agent Jordan Shaw states that the gun is a .45 caliber that they would be sending to ballistics; however the gun that investigators retrieve is a Desert Eagle which based on barrel length and shape could only be a .357 Magnum, .429 DE, .44 Magnum, or .50 Action Express.
Castle makes pancakes because the eggs have expired. Since Castle is often shown whipping up gourmet meals, he should know eggs are an important ingredient in pancake batter. (She could have had a mix that only requires adding water (e.g., Krusteaz))
Castle explains to Alexis and Martha that Conrad shot himself with his right hand, meaning that he couldn't be the serial killer. In the clip from the window, Conrad shoots himself with his left hand. Correction: The person in the window was holding the gun in his left hand. When they found Conrad, he had the gun in his right hand and had been shot in the right side of the head.
When decoding the book code, the various characters speak the word within a couple of seconds after finding the correct page. The second part of the code required counting the word number from the start of the page, yet they were able to do this even with words numbered as high as 204.
Special Agent Shaw says the killer was extracting formaldehyde from embalming fluid to make "cyclonite, a near military-grade explosive". First off, cyclonite, AKA RDX, is the prime ingredient in C4 and the most powerful of the commonly used military explosives. Secondly, he would have a lot of bother purifying and converting the formaldehyde into hexamine, which is then turned into RDX. Hexamine is sold by the pound at hobby stores.
Castle has made it clear that he hates when people misuse the word irony, yet when he holds up the paper, he says, "talk about irony!" when in fact the heading was not ironic, it was just coincidental.
At the end, when Castle is on the phone with Beckett and the bomb goes off, Castle moves his phone away from his head and the audience can clearly see that the phone is facing the wrong way.
When she first appears at the carousel she tells her assistant to rope off a 10' circumference around the carousel.
The circumference is the distance around the circle, so a10' circumference would be a circle with a diameter of less than 4'. She should've said a 10' radius.
The circumference is the distance around the circle, so a10' circumference would be a circle with a diameter of less than 4'. She should've said a 10' radius.