A Father to His Men: Becomes indisputably true during his brilliant Churchillian speech right before the final battle.
Authority Equals Asskicking: Justified, as Whitmore was apparently a fighter pilot in the Gulf War, and is still relatively young at the time of the invasion.
Badass In Charge: Served during the Gulf War, a skill that comes in handy. Even without this skill, his personality is still pretty badass.
Chekhov's Skill: See above: Whitmore's tour of duty as a fighter pilot in the Gulf War.
The Eternal Churchill: And how. Right before the final battle, President Whitmore gives one of the most memorable speeches in movie history, a speech that seems to be deliberately designed to be similar to Churchill's refusal to surrender.
Badass In Charge: Of the United States military, especially once the Joint Chiefs of Staff are obliterated at NORAD by the aliens. Gen. Grey, in turn, answers to an even higher-ranking Badass In Charge: President Whitmore.
Number Two: To President Whitmore. At the beginning of the movie, he requests to stay at the White House alongside the President (it turns out to be lucky. The rest of American generals were apparently killed by the aliens after they evacuated to NORAD). Throughout the movie, Grey is unfailingly loyal to Whitmore and might be either the new Secretary of Defense or even the new Vice President at the end, given the fact that the former VP is dead and the former Secretary of Defense was unceremoniously fired.
Obstructive Bureaucrat: Does nothing but provide bad advice to the President, and withholds crucial information (regarding the Roswell crash and Area 51) that could have been more useful had it been divulged earlier.
The Scrappy: Both to viewers, and in-universe, to the point where a furious and exasperated President Whitmore finally fires him.
What an Idiot: OK, so you're the Secretary of Defense and an entire fleet of alien spaceships shows up and float ominously over the world's major cities. As the former head of the CIA (it's stated somewhere in the movie that Nimzicki was this), you became privy to the fact that Area 51 has indeed been housing a crashed flying saucer and alien corpses and been studying them and their tech for decades. Do you choose to immediately inform the President about everything the research had discovered in order to better inform his decision-making? Apparently not.