Darren Cross' plans to sell the Yellowjacket and his version of Hank Pym's research to HYDRA is foreshadowed rather early on in the film, when he presents his PR video promoting the technologies involved. What becomes evident is how their intended uses are similar to Project Insight in practice and in a sense far more insidious than a fleet of automated and compromised Helicarriers ever could. Highlighting how much HYDRA is still intent on following-up on its schemes even without S.H.I.E.L.D.'s resources. As well as Cross' own dealings with the organization. Also foreshadowed by the fact that the man he's most interested in selling to was a former S.H.I.E.L.D. director who was very intent on replicating Pym's technology, which should have set off red flags in any savvy viewer's head.
Darren Cross' name is even an example. His entire arc is about leap-frogging over lines that Hank Pym himself DAREN'T CROSS.
Both this and in a way Fridge Sadness. Hope is never referred to as Hope Pym during the film despite being Hank's daughter, her last name being Van Dyne, like her mother's. With the effect that Janet's death had on their relationship, her having her mother's maiden name (which she likely changed herself) further emphasizes the distance the father and daughter have.
So, both Michael Douglas and Paul Rudd are 5'10". It seems like a nice bit of casting to explain how the suit fit them both. Then the actual film reveals Hank has been profiling Scott, possibly for years.
Related to the above his how easily Scott is able to get in and out of the suit despite having no idea what it is or how it works the first time he does it as well as the second time, when he does it in under ten seconds. Hank is, if nothing else, a terribly practical man and most likely designed to suit to be easy to get in and out of. He may even use a subtle version of its shrinking power to make it slightly bigger and easier to slip into until all the seals are engaged at which point it shrinks to a perfect fit.
This is almost exactly how Spider-Man's Tony Stark-provided suit works.
The Falcon's goggles allow him to see Scott when he's shrunken. It makes sense since flying high in the air any target would look ant-sized so he would need specialized eyewear to spot them.
And it lets him live up to his superhero name, as falcons have incredible pinpoint vision for spotting moving prey at a distance. Some smaller species even prey on insects.
Since one of Pym's contemporaries in the early days of S.H.I.E.L.D. was Howard Stark, Tony's father, it's entirely possible that Howard considered the possibility of Hank becoming an enemy (or someone else cracking the secret of the Pym Particle) and developed tech to locate individuals that could shrink down to the size of an insect... tech he might have stored at a facility that was later repurposed as the Avengers' headquarters.
Hope told Scott to use thoughts of his daughter to concentrate and focus enough to be able to command the ants. Later, thinking about his daughter is also what lets him focus enough to figure out a way to escape the sub-atomic realm.
A bit funny as well; Scott fought and defeated an Avenger, who later (sort of) recommends him to their leader. Back in the old days of superhero comics, wannabe heroes would sometimes break into a team's headquarters and/or start an fight with them to try and get the team to let them join (Hawkeye once did this to the Avengers themselves, and Vision got recruited this way, too). Seems like charging into someone's base, fighting them and successfully stealing their stuff (with good intentions) really can get you recruited.
At the start of the film, Cassie liking the ugly stuffed rabbit seems like her just liking a gift from her father, but at the end she shows herself to be a Nightmare Fetishist. Her mother questions if she actually likes it, but Scott got her something that he knew fit her interests.
It goes the other way too. When we first see the rabbit, along with Paxton, we can assume Scott either shopped at the last minute or didn't have any money for a higher-quality toy (or both). But he actually took great care in choosing Cassie's gift.
It nicely lays the groundwork for Cassie adopting the giant ant as a pet, too. Many young girls would have found it too ugly or scary.
Howard Stark allowed Hank to leave S.H.I.E.L.D. without any resistance or even last attempt to talk him into giving up his research. It seems odd, but Howard (and possibly Hank) knew HYDRA had infiltrated S.H.I.E.L.D. at that point. Pym leaving gave Howard the perfect excuse to keep one more weapon out of their hands. And given the time period, this might have helped prompt HYDRA to eliminate Howard outright.
Although it's never stated, it's clear that Cross has some serious martial arts training. Scott's got years of prison experience and training from Hope, and more experience with the suit. Cross relies on his lasers a lot, but he's still throwing punches. Even with the risk of killing someone if you can't control your punches in the suit (not that he likely cared), Cross seems a good enough fighter to make up for not having experience in the Yellowjacket suit.
When the Pym Technologies building starts to explode, it suddenly appears to implode instead. Why? Remember where those explosives were planted—in the Pym particle vault. The whole structure shrank away to nothing.
Scott rescuing himself at the end is only possible because of his Masters in Electrical Engineering and spending time upgrading all the wiring in the suit. While he may not understand the sciences behind the process, he understands how the suit applies that science and was able to devise a work around. Also, given that he believed the regulator was a throttle point for the suit's power, it's possible that he can work with Hank in expanding the scope of his powers to become Giant-Man. It also helps that he had the Pym Particle disc to substitute for the fact that his reserves were burned out during the shrinking process.
Hank still throws a mean punch, even at the age of 70 (if we're assuming he's the same age as Michael Douglas at the time of filming). He clearly was fit while operating in the '70s and '80s, but age should have taken a toll on him by being inactive. Except, his house has an elaborate and modern gym in the basement. He's been keeping fit! It's unlikely it was for Hope, due to their relationship and the rushed time of their plan, and the equipment is up to date, so Hank's been using it.
Hank mentions that the suit "takes a toll on the body" and he can't wear it again without permanent, possibly lethal damage. Seems likely he keeps in shape to stave off whatever effects the suit had on his body over the course of his superhero career.
Lang's manager sorrowfully says "Baskin-Robbins always finds out" when he's forced to fire him after the company discovers his criminal past. When Lang gets back to his residential hotel and tells Luis what happened, he repeats the line verbatim, which seems to imply he or one of his friends tried to get a straight job with B-R and got "found out" too.
It's mentioned that Luis went to jail for stealing a pair of smoothie machines. Presumably he stole them from a Baskin-Robbins, and they "found out".
In real life Baskin-Robbins makes a point of hiring and offering second chances to convicts and Scott's manager mentioned he found out the truth of Scott's past. He was fired not for being a convict, but because he lied on his application.
Due to this movie being stuck in Development Hell for 8 years, Hank Pym is not the creator of Ultron in the MCU. However, he was both the father figure for Darren Cross and the inventor of the technology Cross uses. And not only does Yellowjacket have daddy issues with Pym very similar to Ultron's, but his movie design has a face similar to Ultron's classic design.
Hank has a distant relationship with his talented "son" and daughter, much like Howard Stark did with Tony. Not So Different, really.
Luis whistling "It's A Small World" in a movie about shrinking to the size of an ant. His vans distinctive horn is also a stealth nod to the movies insect motifs the tune is La Cucaracha, aka, The Cockroach.
Hank explains to Scott that using Pym Particles without a protective helmet messes with your brain chemistry and, given the fact that he probably tested the particles on himself, it's likely that he found this out the hard way. Combined with the pills that he is seen to carry with him at all times, it's likely that this is a nod to the comics version of Hank and his history of mental health problems.
Why does Darren Cross experiment on adorable lambs rather than rats, as Hope suggested? Shrinking is proportional to the original size of the subject, so it would be much harder to observe a shrunken rat rather than a shrunken lamb.
Why does Siri play "Plainsong" instead of "Disintegration" as was said? Don't forget that Disintegration is also the name of the album the song is on. If you ask Siri to play it on your own phone, the album will play instead of the specific song, beginning with the first track — which is "Plainsong".
The return of John Slattery as Howard Stark. When did he last appear again? In archive footage only, where he divulged the secret of the Stark Expo. The other films probably have some mention of Hank's technology as well, and Tony Stark would be paranoid enough to take precautions - and that's why Falcon is somewhat prepared to fight Ant-Man.
A small one, but it's been noted that "Antony" is actually female. However, when you think about it, Scott knew nothing about ants when he chose the name, and even after that only learned about their uses. He just has no way to tell.
Besides that, the few female names that start with "Ant" are far less common and less likely to be known.
When Hank emphatically insisted that the Avengers not be contacted for assistance in preventing the sale of the Yellowjacket, he wasn't just talking about how he quit S.H.I.E.L.D. in order to keep the Pym Particle out of Howard Stark's hands. He was also referring to how Tony Stark insisted on screwing around with a powerful technology - the scepter - and accidentally created Ultron. That makes Hank seem positively prescient and Tony sublimely stupid, given how S.H.I.E.L.D. screwing around with the Tesseract: 1 (summoned Loki, 2 (collapsed several dozen square miles of the Mojave Desert into a sinkhole, and 3 (led to the Chitauri invasion of New York. The Avengers proved they couldn't be trusted with the particle, the government proved they couldn't be trusted with the particle, so it was Up to Him to deal with Cross.
Pretty sure Tony has PR people to make sure information like that didn't leak to the general public. Ultron's creator was most likely not made public and since it chronologically happened after the Winter Soldier, Tony's involvement in the creation of the Ultron could easily have been kept between the team. Considering the good intentions Tony went in trying to make Ultron, it's possible they decided to protect Tony from the backlash. Tony had nothing to do with S.H.I.E.L.D.'s experiments on the Tesseract, so I'm not sure how Hank would think that Tony did? Also Tony wasn't even the only one to create Ultron. Bruce Banner had a hand in it as well - as did Wanda for putting the image in his head of all his friends dead. Ergo the creation of Ultron is in Banner, Stark, and Maximoff's hands, not just Stark's. My assumption was that since Tony acts the most like Howard in public and took over Howard's company with such vigor that even Obadiah thought the best way to oust Tony was to murder him that Hank assumed Tony and Howard were cut from the same cloth. Your suggestion makes no sense chronologically (even so since S.H.I.E.L.D. never found out Tony was Ultron's creator, it wouldn't matter if their secrets were dumped on the internet), nor fits with the MCU canon.
The point is that Hank had his suspicions about Stark and S.H.I.E.L.D., both of which turned out to be correct. That he never learned they were correct is just his bad luck.
Cross uses S.H.I.E.L.D. archival footage of Hank in action as Ant-Man as an opener for the Yellowjacket project, and no one seems particularly surprised to be seeing it. Stuff like that is probably everywhere post-Winter Soldier, and even sets up the plot; until Cross had evidence that Pym was actually Ant-Man, he was content to simply run Pym's company and handle his projects. Afterwards, it would have renewed Cross' obsession with the Pym Particle and been the impetus for pushing Hank out of the company so that he could have deeper access to the company archives.
The physics-breaking power of the Pym Particle; on the surface, it just makes things smaller. Simple enough. However, a shrunken user can knock out a man by punching him (and is implied to have to use extreme care or his fist and body will simply tear through human tissue like a bullet), but can be light enough to run on top of a gun barrel without the wielder even noticing, while an inattentive user remains heavy enough that falls can shatter bathroom tile or smash through floorboards - without suffering any fall damage more severe than getting the wind knocked out of them. The real superpower of the Ant-Man suit seems to be some form of semi-conscious control of the user's inertia, mass and weight while shrunk. Heart Is an Awesome Power, indeed.
Some would question the need for Scott to smuggle shrunken high explosives into the Pym Technologies building only to re-enlarge them at critical areas throughout the structure given the physics explained in the movie, where a force is magnified by applying the same force over a smaller area, e.g. an Ant-Man punch, one might assume that the same result could have been achieved by simply carrying in a single payload of enough shrunken explosives to level the whole building. However, Pym Particles have inconsistent effects on inorganic objects; the tank Hank carries as a keychain is a real Soviet tank capable of ramming through a building, and a Thomas the Tank Engine toy accidentally grown to human scale during the final fight does the same despite being a plastic toy. Given that kind of absurdity, re-enlarging the explosive would simply be good sense, as everyone knows how they'll perform.
The sensor grid in the Avengers training facility goes off when Scott lands the roof while shrunken. Is it because it can detect objects as tiny as an insect? Not likely, or it would go off all the time. The sensors on the roof probably detected the force of a full-grown man landing on the roof, which could have just as easily been a HYDRA spy or assassin that got dropped in. No wonder Falcon finds it suspicious.
It's been noted that Ant-Man, if portrayed realistically, would have a hard time seeing, since light waves would be too long for his eyes to work correctly, and that his voice would be too faint and high-pitched to be heard. Ant-Man's mask must not only protect him from the effects of Pym Particles, but also contain equipment that converts visible light into wavelengths that he can see, and voice modulation to allow him to be heard. The last part has basis in reality — deep sea divers spend days, even weeks, living in pressure chambers calibrated for the depths they work in so they can go in and out of the water without having to spend hours acclimatizing. The divers breathe helium-rich air while in the chambers and in the water and their voices change pitch accordingly. Their voices go through a modulator when communicating via radio so that the people on the surface can understand what they are saying. They simply have to get used to speaking to each other like chipmunks during their off-hours, however.
The keychain tank is a T-34, a Russian model used in World War II and the Cold War. So why does Pym have it, and not an American tank? Watch the footage of Ant-Man fighting in the 80s. It's the tank he's fighting back then. Pym could've easily shrunk it then and taken it with him.
Hope can appear rather mean-spirited, considering how lethal the Pym technology is and how cautious Hank is about using it. But the point is, she hasn't really witnessed how dangerous it is. Once she learns how her mother died and sees how unstable Cross has become from using it, she's a little more understanding to her father.
During the uncontrollable-shrinking sequence, just as Scott descends beyond the fractal/crystalline level of sub-atomic structure and into the blackness of the Quantum Realm, there's a brief shot of one last crystal-like form in which Scott's own image fans out as reflected duplicates, their forms blurring as if his deep red suit is a stream of liquid. The impression is that his form is flowing because Reality, itself, is breaking down as he penetrates the Quantum level of the cosmos: an impression enhanced by his collective images' resemblance to the flowing, deep red fluidity of the Aether, the Infinity Stone which embodies the Reality he's effectively slipping away from.
While it eventually succeeded, who knows many lambs or other animals Cross sacrificed just to test out the shrinking ability? Or, as was the case with the man who criticized the Yellowjacket idea, who knows how many people he shrunk when not pleased with what they told him and watched them turn into a splat of mush on the ground.
Cross knew that Lang broke into Avengers Headquarters. He could guess the other parts of the heist because he is familiar with the people involved, but to know about that part he would need someone there. The Avengers have a Mole, and since Cross was working with HYDRA, it's almost certainly a HYDRA mole. That, or they're keeping a very close eye on them, despite their advanced tech. Or both.
Janet van Dyne (Wasp):
While, theoretically, Pym's wife could still be out there somewhere, one has to keep in mind that she disappeared decades ago. She surely would have starved to death, unless being outside of time prevents that.
Or unless there's something that manipulates time they could use to get to her... like an Infinity Stone.
Could also be that Hank wasn't wrong when he said that time loses all meaning there. It's widely understood that time is not a universal force and really only exists within our perception of it. If Janet is trapped in a place where all the rules stop applying, she could essentially be stuck out of time. Which would make some fans happy as it would allow them to bring Janet van Dyne in as the Wasp, and it could even lead to a subplot of Captain America and Wasp dating like they did in The Ultimates, since both would essentially be heroes that found themselves outside their own era.
During the Quantum Realm sequences, there are brief flashes of... this.◊
Cross had already sold the Yellowjacket designs to HYDRA by the time the heroes reach him, and Carson made off with a vial of Pym Particles, meaning we likely haven't seen the last of the Yellowjacket. Note that Yellowjacket's suit turned out to be pretty formidable even when it wasn't utilizing its shrinking power. Even without the particles, HYDRA may have gotten a lot more dangerous just from the suit itself.
Now either Hank understands all too well how hard it is for convicts to get jobs and just waited, but he seemed to especially expect Scott would fall back on old habits when times got tough. One can't help but wonder if he possibly tipped off Scott's boss about his past. Certainly very possible with today's technology that the boss found it on his own, but the timing seems very fishy. Yes, Hank had the goal of protecting people, but this is all too real for convicts genuinely trying to go straight only to sabotage themselves.
Exposure to Pym Particles without a proper helmet apparently affects one's mind, and wearing the suit too much is also dangerous (Hank says he can't risk using it again himself). It's possible part of Cross' madness may not have been himself, and the other users of the Pym particules - Janet, Scott or Hope - may also be in danger of losing his mind if they use the suit too much.
If Hope had been in the suit and like Scott, ended up getting stuck in the sub-atomic realm in order to defeat Cross, she would not have had the electrical engineer skills that allowed Scott to improvise an escape and like her mother be stuck permanently, which was exactly what Hank feared would happened.
While it's played for comedy, it's actually very very lucky that Scott's first hurled growth-disc landed on one of the ants. Had it instead collided with the bedroom floor, Cassie's entire house could've been leveled by the sudden expansion of the wooden floorboard it struck, and anyone on the upper stories of the adjacent houses might well have been crushed by the abrupt protrusion of several hundred feet of enlarged plank from either side of the wreckage.
Cross made a working powered armor. Not only that, a powered armor that flies and has lasers. Even without the shrinking abilities, it's highly dangerous, and seems to not lack any of the power issues Stark suits do (in having to rely on an Arc Reactor). Even the HammerTech suit we see Diamondback sport in Luke Cage (2016) lacks those abilities. As of Civil War's 2016 setting, it only took six years since Iron Man debuted for Tony's effort to keep that level of technology from others.
The Pym tech works on shrinking and enlarging people. The shrinking must have been akin to compression. Frank got shrunk and turned into a blob, with his body exploding from the pressure. Cross also died in a similarly gruesome manner, with his body clearly being breaking down. It's not hard to see how that could affect the body and the mind.
The enlarging similarly should be like stretching your body out too, with Scott being a bit out of it after the Civil War fight.
Those cute little crazy ants that seem so much less menacing than the bullet ants? They're an extremely invasive species which has been decimating the forest-floor wildlife on Christmas Island and other isolated habitats they've managed to reach. Better hope Hank's kept a very close watch on his captive colony's reproduction and not let any queens get loose, or the native bugs and small vertebrates of San Francisco are in serious trouble... not to mention the city's electrical grid.