Other mistake: It is said G. Callen has lived in 37 foster homes between the ages 5 and 18, the longest ever having stayed in one is 3 months. 5-18 is 13 years, meaning even if he had lived 3 months in EVERY foster home, it'd have to be a minimum of 52 foster homes. Since 3 months was the longest, it is logical that the others were shorter therefore the number would have had to be much higher.
Continuity mistake: Episode 1-7, "Pushback": At the beginning a person is shot in the back of the head during a surveillance. The camera is filming a man and a woman on a boat at a marina. The feed is being played in real-time on the laptop. The killer starts to gather all the recording equipment, including dismounting the camera off the stand. The killer called the man on the boat to say "it's done". The computer screen shows the man on the boat leaving the boat even after the camera was dismounted.