Continuity mistake: When the scientists are walking through the fog towards the sphere shortly after it has landed in Central Park, we see them walk through many lines of trees before reaching the sphere. Camera cuts to a different angle, when the fog has all cleared and we briefly see behind the scientists and it only shows one line of small trees quite a bit away, not the lines of trees they were walking through before.
Continuity mistake: When Helen and Jacob walk out from under the bridge, at the very end of the movie, we see footsteps being made in the metal "sand". When the camera pans to a shot from behind, the footsteps made in the sand are gone.
Continuity mistake: When Dr. Benson is being escorted from her home, the headlights of both lead motorcycles are on. A few moments later, while on the highway, the headlamp on the right bike (looking at the screen) is out. It is back on again in the next scene. Rather odd, since on all modern motorcycles, the headlamp comes on with the ignition.