Castle initially tells Becket they can't get married in September because he has to travel that month. The only days he would be available that month would be on Mondays. The series airs on Monday nights in North America.
The roller coaster crime scene is at the Coney Island Cyclone in Brooklyn, New York City. However, the scene was filmed on the other side of the US in the Hollywood area using a different wooden roller coaster: the old Colossus at Six Flags Magic Mountain. Whereas the Cyclone is a single-track roller coaster with no other coasters within its immediate terrain, Colossus was a larger, faster, dual-track coaster that shared overlapping space with Goliath (the blue structure bars of Goliath are evident in several shots in this episode). To roller coaster enthusiasts, both the Cyclone and Colossus are considered legendary wooden roller coasters.
Here and in Hunt (2013), James Brolin effectively plays a man of action, a Bond/Bourne action figure. However, the 73 year-old Brolin does nothing more strenuous then stand up and walk five feet.
Both Nathan Fillion and James Brolin appeared in Community, although not in the same ones. For the latter, he also plays a character who has difficult relationship with his son.