At the end of the episode when everyone compares the case outcome with sports, Kevin Ryan says "So what? It's like soccer. You score in our goal, it's still our point". This is not true. If Castle and Beckett score in Ryan and Esposito's goal, it is actually Castle and Beckett's point. This may have been a mistake by the actor or an error in the script. If Ryan had said "So what? It's like soccer. You score in YOUR goal, it's still our point" he would have been factually correct, that would be classed as an own-goal and Ryan and Esposito would indeed get the point.
When being interviewed on BBC Radio-5 (discussing Absentia), Stana Katic said she played soccer as a schoolgirl, one assumes she must have known the rules, so it appears surprising that she let the mistake remain in the script - because she was in the scene and would have heard the error.
When trying to get a confession, Esposito claims that New York is still a lethal injection state. However New York abolished the death penalty in 2007.
Castle and Beckett intercept one of the suspects at the "9th and Broadway Building", with the building's name clearly marked. The two streets do not intersect in Manhattan. However, the 9th and Broadway Building is a well-known piece of Los Angeles architecture.