Being based on a historical Moment of Awesome, this film has quite a few. Col. Pluskat, spotting the Allied invasion fleet bearing right down on him, shouting on his phone, "You know those five thousand ships you said they don't have? THEY'VE GOT THEM!"
The fact that the real Werner Pluskat was actually a military consultant for the film only makes that scene all the more awesome.
Dwight D. Eisenhower - against his own cautious nature - gives the order to go. This is so audacious a move for him that the German officer trained to play as Eisenhower for war games didn't think the Allied commander would do it.
Not related to the movie but in Real Life, Eisenhower wrote two letters to be read. One to the troops, commending them on taking a risky operation. The second was a letter in case the invasion failed, in which Eisenhower was willing to accept the blame ("It is mine alone.") The second letter was never read because Normandy was successful, and was almost discarded except for a junior officer who found it. The second letter - highlighting the responsibility of leadership - became just as famous as the first letter.
General Roosevelt, upon finding his Utah Beach landing is too far off-course, decides to "Start the war from right here" and guides the rest of his forces to that spot. In Real Life he even reconned the area with minimum cover, risking his life. His decision proved right as the improvised landing site was actually easier to deploy troops than the planned site.
He insisted on leading the landing himself - even with his frail health that would kill him a month later.
The bagpiper Bill Millin. The Real Life counterpart later met with captured German snipers and found out none of them would shoot at him because they all thought he was too crazy to be marching about playing that thing.
The Free French commandos retaking Ouistreham. To elaborate, they charge through the town, cutting down everything in their path until they're finally stopped by a well fortified position with an anti-tank gun and a number of machine-gun nests. The Major in command runs back out of the town, through the killzone, to find a tank to help them break the stalemate. while he's gone, a bunch of elderly nuns walk all the way to the french commandos' position to provide first aid. Then the major comes back with the tank and it's all over for the germans. Cheese-Eating Surrender Monkeys my ass.
The D-Day landings as a whole are a CMoA for every Allied soldier - American, Canadian, British, French - who participated. Those who survived and those who didn't.
John Howard as his troops holding Pegasus Bridge - "Hold until relieved."
Luftwaffe Colonel Josef Priller. With his entire air wing having been moved back the day before to airfields out of range of the beaches, the only two German fighter aircraft available on D-Day were his own and his wingman's, Sergeant Heinz Wodarczyk. And so the two of them flew out — by themselves — to do an air attack on the entire Allied invasion. The two FW-190s strafed Sword, Juno, and Omaha beaches, while flying through the combined antiaircraft fire of every ship in the invasion fleet, until they ran out of ammo and returned to base unharmed. The comment of one of the British sailors witnessing this;
Leading Stoker Robert Dowie, HMS Dunbar: Jerry or not, the best of luck to you. You've got guts.
"The Luftwaffe has had its finest moment!"
And that really happened. Though not portrayed in the film, they were also both badly hungover at the time.
At the first bombardment, one of the locals goes nuts with happiness and starts waving a French flag, even as some of the shells hit his house.