In the tea party scene (around 23 minutes) when the unsub is handing out the tea cups, "Sally's" hand is laid on the table. Initially the unsub lays her hand palm down, but when the unsub gives her her tea cup for a brief moment her hand is shown palm up and then suddenly it's palm down again without the unsub moving it.
Paralysing agents such as atracurium paralyze ALL muscles including those that makes us breathe. So whether or not the unsub gave the victims a sedative or not they would die within minutes of receiving the paralysing agent.
As with most devices of convenience in TV shows. the stun gun used by the unsub incapacitates her victim. In real life, they hurt a lot, and cause loss of muscular control, but only for a few seconds.
One of the victims has Diabetes. In this episode a common mistake in many shows, Insulin is treated as a cure all for people with Diabetes and that they will die quickly without it. The more likely scenario is they would slip into a coma after days or weeks without insulin. If they had insulin earlier that day and did not get a chance to eat they would get insulin shock and wouldn't be very responsive at all.
At the end, Spencer says "check mate in 12", but they make at least 15 moves before the shot fades to black.
"Checkmate in 12" refers to the number of moves one player makes (the eventual winner), so the total number of moves by both players would be 23.
The New Jersey license plates on the cars are shown to have a bright yellow stripe of about 2 inches across the top with the remainder of the plate being white. In actuality, New Jersey plates have a more beige-yellow tint at the top which fades very gradually toward the whiter bottom, so that there is no noticeable line differentiating the colors.
Around the 15 minute mark, while in the truck the unsub pulls out a taser and shocks the woman, but if you look closely you can see that the taser never actually touches her.
When a chess game ends in checkmate, the loser does not knock the king over since this indicates a resignation. This is a common error in TV and film. Resignation has to happen before checkmate is reached, not after.