Factual error: A theater marquee is visible promoting the showing of a film called Tribeca Follies. The acronym "Tribeca" - an amalgamation of "Triangle Below Canal [Street]" - didn't come into usage until the 1970s.
Other mistake: When Alice's ship is being chased, she orders her crew heel to port (turn left). Instead, it turns heel to starboard (right).
Continuity mistake: The location of the FireBrand tower keeps changing throughout the film. 1:30 - the tower is in Lower Manhattan, south of the World Trade Center 2:55 - As Kevin Spacey lands, the tower has moved closer to the World Trade Center (side note - the shot immediately before this showed him falling towards midtown Manhattan, not the tower) 3:45 - the tower has moved further north towards midtown 4:50 - the tower appears to have moved back to the position it was in at 1:30. 5:25 - the tower has moved back to it's position at 3:45. 53:25 - We are given a view of the tower from their Central Park penthouse, and it has apparently moved much closer to Central Park (right next to One57 on the other side of Manhattan island) 56:45 - the tower has moved back down to its position at 3:45 and 5:25. 1:17:38 - I'm not entirely sure about this one, but you can briefly make out the two pools of the World Trade Center memorial, which would put the tower at its location at 2:55. 1:18:00 - the tower has moved to the exact location of One World Trade Center (therefore making that building disappear). 1:18:05 - the tower has moved back to its position at 2:55 (now One World Trade is visible).
Other mistake: Duke is running through the city while dragging Max by his leash. A close-up shows Max being pulled between the bars of a metal fence, but the gap is much too small for Duke to have passed through.
Continuity mistake: At breakfast in the BFG cave the bottle of frobscottle is taken from the table by the big bad giant when he says "I is taking this", only to show up again when Sophie clambers out the shnozcumber.
Other mistake: When Warwick Davis shows Joe the form he's tricked his father into signing to allow him to transfer schools, the form is shown full screen. The "home" phone number is the same as that used in the school's letterhead, and there is text that says"insert name of fictitious school here." Also in this scene the name of the headmaster and phone number is visible, but none of those details match what is on the school's advertising board a couple of scenes later when Joe starts at his new school.
Continuity mistake: The sun angle changes several times during the chase sequence when the dragon is on the flatbed truck.