When Danny Reagan first meets Lt. Carver, she is talking and laughing with Baez as they both look at a case file. The case file is open, then closed, and then open again as the three of them have a conversation.
Nicky mentions that she got into 7 out of 10 colleges she applied to. This episode takes place in October and college admissions letters don't go out until the new year. Columbia especially doesn't post admissions decisions until April. There is no way she could know if she had gotten in at this point.
When Jamie's trainer rides up on a motorcycle at the end, Jamie asks if it's a late 70's Triumph, and mentions how that vintage of bike requires a lot of work to shift with the right foot. It's how Jamie realizes his trainer was faking his injury. However, all Triumphs after 1974 had their gear shifter on the left like modern bikes. The bike his trainer rides up on is a late 60's British bike with the gear shifter on the right.