The victim's husband says that his wife's Social Security number matches that of a child who died at 3 months of age in 1963. Children were not routinely issued Social Security numbers prior to 1986 until they started earning income as teenagers.
During the game of Texas Hold 'Em between Castle, Beckett, the Mayor, Montgomery, and Markway, players begin betting randomly, and without regard for whose turn it is to legally bet. Montgomery legally takes a turn when he folds after all the other players have called. Then, the Mayor raises out-of-turn, skipping Markway, Castle, and Beckett. Montgomery folds in-turn, but the Mayor again skips Castle and Beckett by folding out-of-turn. Play continues correctly during heads-up. The funniest thing about this scene is that if you only take into account what's happening on the screen, the Mayor appears to raise his own bet, then fold even though no-one else has bet.
When she is being interrogated, Lee Wax (Joanne Kelly) says Cynthia waited for the ship to be empty. A ship is never left unattended. There is always a crew onboard standing watch even while in port. Any Merchant Mariner or Naval personnel would pick up on this error.
Esposito shows there were empty bottles of motor oil in the closet, which is usually an amber/honey color but the motor oil in the tub is oil that comes out during an oil change.
When they show the FBI flier for the victim, it says her weight is "14 lbs".
At the beginning, when Castle, Beckett, Montgomery, Ryan, and Esposito are playing cards, they say it will be the last hand and Martha complains that it's not even midnight. After Beckett gets the call about the murder, Martha complains that it's after midnight.