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.
Other mistake: Hetty's image appears in a mirror talking to Kensey who is getting changed for an undercover assignment when Kensey walks out of the changing area the mirror is on her right but Hetty is in front of Kensey and could not have appeared in the mirror.