When George is President and the spaceships are approaching, his military advisor tells him he should counterattack. A counterattack is only possible if someone has first attacked, which the spaceships had not. Not a goof: This is George's fantasy, and he doesn't know about defensive tactics.
When George is imagining himself as President, the view from the Oval Office window is incorrect. The Capitol Building is not visible from that window, nor is it that close. Not a goof: This is George's fantasy, and he doesn't know the layout of Washington.
After George buys a newspaper he enters his office. The door with his name on it has no door latch, revealing it to be a prop door.