Further establishing how badass Hank is; when he walks out on SHIELD (with numerous government secrets and extremely advanced tech in tow), both Howard and Peggy decide that they'd be much wiser just to let him go. In other words, Hank Pym is badass enough to intimidate all of SHIELD.
A subtler badass moment for Hank. He walks into his company after years of absence and a security guard asks for his ID.
Hank:[points to an oil painting of his younger self on the wall] I think that will suffice.
Howard gets one in the opening scene as well. When Mitchell mocks Hank for failing to protect Janet, Howard visibly reels in disgust, and after Hank bloodies Mitchell for the insult, Peggy stops the attack while Howard just sits there. And when the bloodied Mitchell shoots him a reproachful look for it, Howards ends him with one line:
Howard: Don't look at me. You said it.
When Hank punches a smug Cross in the face. Cross claims that he knew the punch was coming, but didn't expect Hank to hit so hard.
Cross: Wow. Wow.[briefly makes a 'not-bad' expression] I mean, I saw that punch coming a mile away, but I expected it would be all pathetic and weak. Hank: Well, you thought wrong.
The footage detailing Hank's exploits as the original Ant-Man. Yes, you're seeing it correctly: those are tanks being blown up and soldiers being knocked out or shot up, all on a military base. Not so lame now, right?
Scott breaking into "some old rich guy's house" sets up how excellent his burglary and improvising skills are. The first hitch is a lock that requires a finger print, so he makes a resin impression from a doorknob and gets by that. The second hitch is trickier: a thick steel door, so he resorts to using ice to make the door explode. Hank wasn't kidding about finding the right guy.
The end of the Training Montage where Scott runs with the ants before taking the lead and getting ahead while they follow really shows that he has become part of an amazing world.
Janet stopping a nuclear missile from hitting Washington by going subatomic.
Scott can become so small that most people have a hard time spotting him, let alone hit him. Falcon still manages to knock him around for most of their fight.
The end of that fight is a moment of awesome for Scott, himself. This is a guy who is still limited in the use of the suit, and is on his first real operation using it. Instead of turning around when discovering that the factory is not an abandoned Stark Industries district but something being used by the Avengers, he powers on. During his fight with Sam Wilson, he holds his own incredibly well, infiltrating Falcon's back-mounted tech to stop his wings and magnifying goggles from working, all while successfully locating and retrieving the device he was sent to get in the first place.
Scott's line summing up the fight.
Scott: Can we just talk about the fact that I fought an Avenger and didn't die!
He's not kidding about the "didn't die" part either. At several moments during the fight, Sam does indeed attempt what would have been lethal measures if Scott were a non-powered opponent, including opening fire with his pistols at point blank range. If anything, Scott's victory was undersold.
Sam Wilson being able to time his punch just right to knock out Scott charging him while shrunk.
Luis knocking out a number of guards during the heist.
Cross revealing how Crazy-Prepared he is when Scott reaches the shrunken Yellowjacket armor ... and Cross smugly lowers it out of its containment unit and reveals that he knew all along what Hank was planning and doing, and turns it into part of his pitch to HYDRA. Shame he didn't guess what Hank is also planning to do...
Cross takes advantage of Scott tending to a wounded Hank to point a gun at his (non-bulletproof) helmet. What does Hope do? Uses her own insect manipulation device to cause a swarm of ants to jam the gun.
Hank is also Crazy-Prepared, revealing that the tank keychain isn't just a decoration. It's an actual T-34/85 medium tank shrunken to a smaller size. This proves instrumental in helping him and Hope escape Cross's vault.
"It was never just a heist!" Cue the destruction of the Pym Technologies building. At first, it just looks like Stuff Blowing Up, but then you realize the building is not exploding, it's imploding!
The final battle between Scott and Cross. The Yellowjacket suit is a military weapon that can kill people from a distance while shrunk and the Ant-Man suit has presumably not been updated for a few decades. Scott still uses his ingenuity to maintain a big enough advantage during the fight that only the Yellowjacket's more advanced features let it stay standing.
A full-size Scott backhanding a shrunken Cross into a bug zapper with a table tennis paddle. Keep in mind that most people in the movie can't properly track a shrunken opponent to combat them.
Some credit also goes to Paxton during the climax: despite being a cop with no powers, he charges into the house the first opportunity he gets with nothing but a handgun. While he freaks out over the enlargened ant at first, he quickly gets over it and almost manages to get Cassie out. Then when Cross blocks off his means of escape, he gets Cassie behind him, intending to protect her even though the villian has the greater advantage.
When the battle moves to Cassie's train set Scott falls back in a forest of carpet. He then charges out with an army of ants as though they're storming the beaches of Normandy.
Scott's ants in general are awesome. Those little guys are as much of a hero as any Avenger and their assistance almost always helps turn the tide from defeat to victory. This includes Scott's fight with Cross, where even though the latter keeps knocking them away, they just keep coming, keeping him occupied and more than a few bullet ants tearing into his suit's electronics (at least partially made of titanium, which even Scott can't break through as seen later) - if they'd hit anything important, Cross would have been helpless to them at that size. Hank and Hope regard the ants as the suit's greatest power and they're absolutely right. It's the one power Cross's suit lacks and that's why he loses.
It gets better when you know the line was put in the script with no expectation that it would lead to anything else, before Marvel and Sony reaching a deal to share the rights to Spider-Man resulted in it being perfectly placed to lead into his first MCU appearance in the very next film.
Hank revealing to Hope the unfinished second Wasp suit in the mid-credits stinger. And then it got better: the title of the film's direct sequel is Ant-Man and the Wasp. Ladies and gents, the Wasp is back.
The reveal in the opening scene that despite all the sexism she suffered back in the '40s, Peggy Carter did eventually get all the prestige she deserved and rose to a top-level SHIELD administrator.
The second Post-Credits scene: Cap and Falcon find Bucky!
During the scene where Scott enters the Quantum Realm, you might notice a certain someone◊ reflected in Scott's helmet. That's right, Janet survived in there for decades!
For what looks just like mere comic relief, much credit must be given to Luis' fellow partners-in-crime, Dave and Kurt, when they show their chops during the final heist. When Paxton and Gale show up unexpectedly and nearly jeopardize the heist by arresting Hank, Dave spots them early using his knowledge of cop vehicles and saves Hank by hijacking their car to distract them. Not only that, when they accidentally draw the cops' ire, the two of them manage to evade them long enough for Kurt to save Scott's behind when he nearly gets fried by a laser trap!