It's hard to remember how much risk this film had. Let's count the ways:
Marvel had signed away the rights to their most well-known properties and was now trying to produce their own films with second-tier characters (before the movie came out, Iron Man wasn't particularly well-known or popular).
Not only that, but Marvel Comics set up Marvel Studios with an 800 million dollar bond obtained by putting their entire catalog up as collateral. If the so-called Marvel Cinematic Universe flopped, a change in management would be the least of Marvel's worries.
Said movie would star an actor who, while acknowledged as talented, had become infamous for his drug addiction problems and numerous run-ins with the law in the lead role and was going to be directed by a man whose last film had been a box-office bomb.
The crew only had a broad outline and most of the dialogue was improvised.
In hindsight, it was the greatest decision Marvel ever made. Iron Man helped boost the character's popularity with the mainstream, convinced Marvel that even their less popular heroes could be box office draws, and propelled the studio to super-stardom. On the Hollywood side of things, it gave Robert Downey Jr. a massive Career Resurrection and launched one of the most influential franchises in modern cinema, which would also become the most profitable film franchise in history.
Complete Monster: In the novelization by Peter David, Obadiah Stane is presented as far worse than his film counterpart. Just like in the movie, Stane is a warmonger and weapons manufacturer who hires terrorists to murder his surrogate nephew, Tony Stark, alongside an entire military squad. Using Tony's seeming death to take over Stark Industries and begin selling off dangerous weapons to terrorists for a profit, Stane later betrays and wipes out his former terrorist partners before attempting to murder Tony with his bare hands. After creating his own suit of superpowered armor and becoming the Iron Monger, Stane slaughters anyone in his way in a mad attempt to murder Tony and Pepper Potts, using a woman and her four children as ammo to attack Tony with. In the novel, in addition to all that, in his prime moment of villainy, Stane completely ignores the fact that the damaged Arc reactor will explode and wipe out thousands of innocents, so hell-bent on crushing Tony that he is willing to take down an entire city in the process.
Crosses the Line Twice: The scenes where Tony kept smacking into things while testing his suit was funny in all the wrong ways. "10% thrust." Splat!
First Installment Wins: Many viewers find this to be the best film in the Marvel Cinematic Universe, or of the Iron Man films at the very least, and it's hard to overcome the perception that Tony Stark is the overall protagonist of the entire MCU (or at least the Infinity Saga) by virtue of being the first hero to be introduced (although Captain America gives him some competition in regards to that). Stane is also considered one of the best MCU villains in the Phase 1 and Phase 2 films (second only to Loki), which were criticized for their bad guys being mostly one-note evil people.
Franchise Original Sin: While many agree it's a very good movie, in retrospect, it set up several of the things that Marvel's movies would be criticized for later on.
The use of The Stinger for a Sequel Hook. Marvel hadn't considered making a franchise of interconnected movies yet, so it came off more as a little And the Adventure Continues moment when you first saw it. But the continued use of them, with two per movie later on, would become grating as it felt like they were more about advertising future movies than adding a meaningful contribution to what you just saw.
The true villain (Stane) disposing of the apparent villain (Raza) before the climax. They got away with it in this movie because Raza wasn't a comics character to begin with and Jeff Bridges' performance was so effortlessly menacing that Stane came off as clearly the superior villain. Later MCU films would repeat this plot point, but with iconic comic characters who clearly had a lot of life left in them, like Crossbones, Baron Von Strucker, Ulysses Klaue, which frequently felt like a slap in the face to comic book fans.
This undoubtedly reached its apex with this movie's own threequel, which infamously tried to retcon away Iron Man's arch-nemesis from the comics in favor of some generic asshole who barely even existed in the source material.
The juxtaposition of humor and action. This movie and later Phase One films were good about knowing when to leave one or the other to the side as needed. Later films would be occasionally criticized for not always maintaining this and reducing the tension of a few serious scenes. Downplayed overall, though, since most will agree that the franchise still runs on a good balance between the two.
The success also put Robert Downey Jr. back in the forefront and made his Iron Man role a big draw for the franchise. This didn't become a real problem until Age of Ultron, where it resulted in Stark getting to create Ultron — kicking Ant-Man out of the position despite his film having been lined up — and not getting his comeuppance until Civil War.
Genius Bonus: Tony's craving for a cheeseburger when he's rescued may seem like just a joke, but if you know anything about Robert Downey Jr.'s story of recovery it starts to take on a larger meaning — RDJ actually credits McDonalds with inspiring him to get off drugs because one day he was driving a car with a "half a ton" of drugs in the trunk, he decided to get a burger. He called it "worst burger of [his] life" and it actually made him reevaluate all of his life-choices. After that, he threw all the drugs into the ocean and checked into rehab. So, rather fittingly, Tony's equally life-changing decision to stop making weapons also involved a burger in some way.
The POV shot of Tony while falling in the iced-up armor is exactly like Rhodey's in Captain America: Civil War. In the very same suit no less.
Rhodey also has an offhand comment, "Look who fell out of the sky!" Ouch.
In the beginning press conference, Tony offhandedly announces that he never got to say goodbye to his father. With a Freeze-Frame Bonus in Captain America: The Winter Soldier, we find out that this is because HYDRA had Tony's parents killed. In Civil War, this is revealed to be a major source of trauma for Tony and finding out that Bucky killed Howard and Maria AND that Steve knew about it effectively kills any hope of a truce between Steve and Tony. Though it swings back into Heartwarming in Hindsight where due to time travel, Tony gets to meet his father in the past and reassure him about having a son.
Doubles as Heartwarming in Hindsight. When Pepper finds out that Tony is Iron Man, Pepper attempts to quit her job, telling him that he will "kill [him]self" eventually, and that she won't "be a part of it.". In Avengers: Endgame, Tony literally kills himself with gamma radiation when he uses his nano-tech Infinity Gauntlet to snap away all of Thanos' forces. Pepper is the last person that approaches and speaks to him at his deathbed.
Another moment: as Tony repeatedly demands Pepper to blow the arc reactor, she eventually says: "You'll die!"
The moment where a tech tells Obadiah Stane "Well I'm sorry; I'm not Tony Stark" takes on a different tone after you've seen Spider-Man: Far From Home, when the same guy shows up again working with Mysterio, the latter of whom's motivated by what Tony Stark previously did to him.
When Tony returns to the United States, he says he wants a cheeseburger against Pepper's wishes of wanting to take him to a hospital. At Tony's funeral in Endgame, Happy Hogan starts laugh-crying, as does most of the audience, when Tony's four-year-old Morgan asks if they can get cheeseburgers. Kid's exactly like her father, in the best way possible.
Rhodey is visibly worried when he finds a dehydrated and injured Tony in the desert, saying, "Next time you ride with me." Rhodey and Iron Man "ride together" again in Avengers Endgame in the final fight, only this time Rhodey doesn't get to save his best friend.
In a conversation early on, Yinsen comments on how empty Tony's life is, a "man who has everything and nothing". 15 years later in Avengers: Endgame, he has a family with a wife, daughter and a child he mentors. There is an enormous crowd of friends and family at his funeral showing just how many lives Tony touched and how much he gained after the cave.
The first thing Tony asks for once he's back home, even before the press conference, is a cheeseburger. During his funeral in the epilogue of Endgame, his daughter tells Happy that she wants a cheeseburger - followed by Happy saying they were her dad's favorite.
At the press conference Tony mentions he never got to say goodbye to his father. In Endgame, not only does Tony meet his father in the past, but he gives him a very heartfelt goodbye, complete with a hug.
In regards to Pepper's line: "You're going to kill yourself, Tony. I'm not going to be a part of it.", while Endgame had Tony willingly sacrifice himself, Pepper still played a part in the final battle, decked out in one of Tony's suits! And he didn't die without his precious wife at his side.
The formal event in the middle of the first film takes place at the Disney Concert Hall. Guess who owns Marvel now? (The Walt Disney Concert hall has nothing to do with the Disney company and was endowed by a private foundation in Walt's name, but it's still pretty funny.)
In this movie, Rhodes briefly considers using the Mark II to fight alongside Tony. In the sequel, the first time he uses it is to fight against Tony. Rhodey's "Next time, baby." line is also somewhat ironic coming from Terrence Howard, considering that Don Cheadlereplaced him for that role from Iron Man 2 onward.
"The truth is... I am Iron Man." Unprecedented in any superhero movie before, its effect is lessened now that none of the supers of the Marvel Cinematic Universe (except for Spider-Man) even have a secret identity.
The fact that Nick Fury arrives in The Stinger to recruit Iron Man for the Avengers is pretty well known now.
Also, the fact that Obadiah Stane is the main antagonist. Even promos that came out around the time of the film's release didn't hide it much. Case in point. And his role as a supervillain was never treated as a spoiler in the comic book source material originally.
Moral Event Horizon: Stane does a lot of villainous things in this movie, but ordering the Ten Rings to kill Tony, the son of his life-long friend just so he can sell arms to terrorists is where he first crosses the horizon. Everything after that is just furthering his personal agenda.
Tony taking a nauseatingly long medical device out of his nose when he wakes up in the cave.
Pepper having to replace Tony's mini-arc reactor was more than a little gross for some. Her comment about pus didn't help, and even though Stark calls it inorganic plasmic discharge, having everything she pulls from his chest dripping with slime, just makes it worse.
Visual Effects of Awesome: The best visual effects work is during the scene when Tony's entire automated workshop dresses him in his Mark III armor, piece by piece, finishing with placing his helmet and mask.