Nathan ad-libbed the line "I still have the taste in my mouth!"
Writers for the show handcuffed themselves and decided it was best for Castle and Beckett to be handcuffed left to left.
Beckett says handcuff chains are "hard cased steel". The writers almost got it right. Low carbon steel is durable, it can take a beating without breaking, but is easy to cut. High carbon steel is hard to deform or cut but is brittle upon impact. 'Case hardened steel' has a relatively low carbon core with a high carbon surface.
In one scene, Castle and Beckett talk about Lanie and Esposito's reluctance to admit they want to be together, despite their wanting to, and wonder why people punish themselves like that. This is an amusing juxtaposition of their own relationship; on one hand, Beckett is aware of how Castle feels about her and, while she has similar feelings about him, she is determined not to admit and act on them. On the other, even though he's professed his feelings, Castle doesn't take the initiative in pursuing it because he's waiting for any kind of signal from her that there's something to pursue.
At one point, Castle suggests getting in the freezer to protect themselves from the tiger. Beckett and Castle were actually locked in a freezer in the season three episode Setup (2011).