Continuity mistake: In the episode "Lost Time," when the professor stands up in the holding cell after Jack tells him that someone saw Skye at 10:30, he slams his chair back causing it to tip over. In the next shot the chair is upright, then when he goes to sit back down, it is again on its side.
Plot hole: Jeremy Garrett is missing and last known whereabouts is a motel in Massachusetts. The Mass. State Police alert the FBI of a "disabled vehicle report" filed the night before. The vehicle's license plate was called in and a tow truck requested. When the truck arrives to remove the vehicle, it is no longer there. Later in the episode it is revealed that the missing person is having an affair with his boss who is also secretly gay. The wife of the boss admits to picking up Jeremy at the motel after intercepting a 1:00 am phone call to her husband hoping to convince Jeremy not to "out" her husband and ruin their "arrangment" style marriage. She admits to stopping along the highway getting out to argue with Jeremy and eventually pushing him down a cliff to his death. The shot of the push has the two standing in the beam of the headlights and only takes about 15 seconds from the two getting out of the car to her driving off after the crime. How could a state trooper investigate a disabled vehicle that is idling with the headlights on first of all and secondly call for a tow truck not only in less time than the vehicle was sitting there but also without seeing them standing five feet in front of the vehicle arguing?
Continuity mistake: In episode "One for All," when they are first at the school looking at the seating chart, Danny states that the teacher said that all the students are in their assigned seats. Malia's name is in the first row second seat, but she is actually sitting in the first row first seat.