A minor moment before that; when Whitmore finds David and Julius in the Oval Office, he wants to blow them off. Julius walks right up to the President of the United States to politely urge him to listen to his son.
Julius comforting David after the failed attempt to nuke the Invaders's ships.
Steve and Jasmine's wedding, made extra heartwarming by David and Connie fully reconciling.
President Whitmore and General Grey's trust in each other to the point of occasional First-Name Basis.
Particularly the moment when Whitmore decides to fly in the final battle.
Grey: Mr. President, I'd sure like to know what you're doing.
Whitmore: I'm a combat pilot, Will. I belong in the air.
The look on Grey's face says it all. He has severe reservations about having his Commander-in-Chief and (in all likelihood) former subordinate to risk his life. But, they're short on pilots and Whitmore does have combat experience. In addition, if they lose, then it won't matter if he comes back or not.
Also, the simple fact that the President of the United States is leading troops into battle.
The farewell scene before Steve and David attempt to infiltrate the mothership. Especially the exchange between David and Julius:
Julius: (hands David a pair of airsickness bags) "Here. Just in case."
David: (hands Julius a yamukel and a Torah) "Here. Just in case."
In the special edition, David tries to find Connie's private cell number. He tries numerous variations and nicknames, but it doesn't come up. Julius suggests searching for "Levinson," even though she didn't take his name when they were married. David types it in to prove he's wrong...and sure enough, "Connie Levinson" appears.
Julius: Hehe, so what do I know?
Also the fact that, despite being rebuffed in his attempt to warn her over the phone, David still drives all the way to Washington to convince Connie in person.
The novel features an extension of the scene with the RAF pilots. As they head for the communications tent, they're joined by an Israeli soldier. The Arabs are understandably nervous, but a few jokes by the British, the Arabs, and the Israeli help to alleviate the tension. As one of the Brits says, forty-eight hours of an alien invasion have done what seventy years of diplomacy couldn't.
Even after Nimzicki has spent the whole movie as full-on Jerkass, Julius still urges him into joining the prayer group Julius is leading.
Nimzicki: I'm not Jewish.
Julius: Nobody's perfect. [resumes praying in Hebrew]
Humanity celebrating their survival, as the movie cuts to an African nation, Egypt, and Australia all with downed City Destroyers.
As they're planning to launch the attacker, Connie tries to talk David out of going. He replies that something may go wrong and may need to think quickly, but punctuates his point with:
"You know how I'm always trying to save the planet? (tosses an empty Coke can into the recycling bin) Here's my chance."