When Dave notices the photograph of the Orb he picks it up to examine it, however, the internal view screen shows the photograph still sitting on the shelf.
When Gina gives him the tomato ketchup, he drinks it and there is some sauce still on his lip. However, in the next scene, where the cat approaches him, the sauce is gone.
The NYPD doesn't have jurisdiction on Liberty Island; it's federal land.
When the captain is back and taking over the ship, the screen shows spelling error twice, first "System Overide Access" and second "System Overide Enabled". However, the correct spelling is "Override" with two R's.
When Dooley and his partner check out the impact site on Liberty Island, the rock in front of Dooley visibly wobbles as only a lightweight object would do.