Continuity mistake: David calls Connie at the White House and she walks toward the divided pane windows, then pulls one curtain to the side. In the exterior shot facing her, the pane's white grille is between the two sides of the curtain, but in the next interior shot looking out, there's only clear glass, though we should see the grille, just as we see both sides of the curtain with her hand holding the right side. Then, in the next exterior shot facing her, it's back to the original with the visible white grille. (00:38:25)
Visible crew/equipment: Boom mic visible, reflected in Barb's motorbike helmet as she talks to Big Fatso.
Visible crew/equipment: In Servo's room, Trace Beaulieu's hand is very visible operating Crow. Watch the bottom of frame when Crow approaches the Interocitor and says "Well, let's see what this baby can do." (00:48:00)
Factual error: Casey arrives at the desert landing in a jeep that is flagged with 4 stars (for a 4 star general) although he is only a 3 star general (as evident by the 3 stars on his shoulder boards). (00:33:30 - 00:35:25)
Factual error: In the scene where Picard opens a viewing port and shows Lilly that she is in a starship orbiting Earth he shows her New Guinea and Australia. New Zealand is missing. (00:42:45)
Suggested correction: Actually when you look at Australia and New Zealand from orbit, New Zealand is a lot further away from Australia then shown on a map, also a lot more south of Australia. A map is a 2D image of a sphere, causing proportions to be off (its well known Africa is a lot smaller on maps than it is in real life). Especially the further south or north you go distances are way off. The depiction shown in the movie is actually correct, in that angle New Zealand is just outside of the frame. There are plenty of pictures from orbit to compare.
Other mistake: Near the end of the closing credits, when the Warner Bros. Copyright appears, you'll see the very first word "All" spelled incorrectly as "Al" in "All material is protected by Copyright Laws of the United States and other countries throughout the world." (01:26:40)
Continuity mistake: When Burt is hiding in the bulldozer scoop, Grady looks down at him from the top of the oil tank and we see that Burt has his knife in his hand. However, in the next shot, we see him pull the knife out of its sheath on his leg.
Other mistake: As Plisken escapes in the hijacked chopper, Quervo Jones picks up a bazooka and prepares to fire on it. As Fast Eddy shoots him through the chest, watch the bazooka. You can see right through the barrel. In other words, there is no ammo in the weapon. (01:25:05)
Continuity mistake: When David goes into the Dodson Hotel to look for Eddie, the glass door he enters through is completely normal. When he runs out chasing Eddie, he goes out the same entrance and this time the right glass door has a huge hole and is shattered. (00:47:40 - 00:49:35)