During Castle's conversation with Jenkins, Jenkins has a trickle of blood next to his lower lip from when Castle punched him. After the last cut to Castle, when the camera goes back to Jenkins, the blood is gone.
In Castle's dream, he sees an automatic pistol fire and eject a straight-walled case. Immediately after, a necked case hits the ground.
After Castle talks to Phillip Bartlett and Bartlett tells him he wasn't a "debate geek," Castle tells Beckett he called the school and the school confirmed he didn't share the debate trophy with anyone. Later, he learns that it was Jafari that he shared the trophy with, but Bilal says they had to replace Castle's memories. The school would still have the record that Castle and Bilal shared the trophy even if Castle's memories were replaced.
When Castle goes to Sunil's Cafe, he questions the hostess about Jeff Powers, asking if she knew him. She replies he is a regular customer, and Castle responds, "very regular, in fact over the past 6 months [Powers] has comes here, without fail, every Tuesday at 6pm" (which Castle presumably learned from Powers' credit card statement). However, on the credit card statement, there is no time stamp noting when he was there. Furthermore, the dates shown are not all a week apart, and only one was a Tuesday. Specifically, it lists the following dates:
11/06/14 (which was a Thursday)
11/13/14 (Thursday)
02/04/15 (Wednesday)
02/10/15 (Tuesday)
02/20/15 (Friday)
02/27/15 (Friday)
03/06/15 (Friday)
03/13/15 (Friday)