I'll give Iron Man this: it tries.
It tries to include female characters and overcome sexist tropes. It doesn't try very hard, and it doesn't do a very good job, but the signs of effort are there.
Disclaimer: I'm not a comic book fan. Although I have picked up some tidbits about comic book plots here and there, I've never read them, so I'm commenting solely on the movie. This is definitely a casual viewer/laywoman's review.
Speaking generally, Iron Man is a really good movie, and I enjoyed rewatching it far more than I expected to. It's got interesting character development and exciting battles and explosions. It skilfully makes us attached to side characters, even the soldiers who appear for about a minute in the beginning, so that we care when they die. It even gets thought-provoking in there amongst all the heroism and smashing of things. Come for the superhero antics, stay for the compelling emotional arc!
But when we look at it through a critical feminist lens, all that falls apart. I did get the sense that Iron Man tried to include women in its story, but it just didn't know how to succeed.
The problem is obvious in the movie's very first scene. You see, one of the soldiers escorting Tony in Afghanistan is a woman. And the movie makes sure that we know it. Women can be soldiers too! Look how inclusive we are, with a female soldier here! Marvel at how Tony's attitude to her changes completely the moment he realizes she's a woman, and how he immediately starts hitting on her! It's pretty painful, and it broadcasts the movie's overall stance on female characters from the beginning: they exist, it's going to try to include them in the story, but stereotypes are too well-ingrained, and it'll fall back on sexist tropes in the end.
For example, the movie does have two named female characters talk to one another (although I think they mostly talk about Tony Stark), so it's at least close to passing the Bechdel test. Except that we don't learn the second female character's name until far into the movie, because nobody really thought to ask, and the main purpose of the scene is for Pepper Potts to call this woman "trash." It lasts about a minute, its the only time we see two women on screen at the same time, and its used for the two female characters to insult one another over a man -- Pepper Potts is just his maid-like assistant, and the reporter is "trash" for sleeping with him.
Worse, this is the scene where Pepper Potts is introduced to us. This is the moment where we're supposed to start liking her as a character and root for her, and her likeability is established through a well-constructed barb against the only other named female character.
And the reporter is another example of the movie almost (but not quite) including decent female characters. She is, after all, insightful, intelligent and successful, and she lays out the truth to Tony at the very start of the movie. She tells him that his weapons are killing innocent people and that he should feel ashamed that his legacy is death... and he then spends the rest of the movie learning that for himself and deciding to use his talents to actually help people instead. So the reporter is right! She's an important character! When we see her in the press conference at the end of the movie, she's the figure reminding Tony of who he was before and encouraging him to do the right thing. Right?
Nope. The movie never treats the reporter as a serious character. Tony dismisses her at the start of the movie, and we dismiss her along with him, mostly because she's the sexy young blonde reporter who criticizes him but then falls into bed with him at the first opportunity. She's "trash," as Pepper Potts says, and we just accept that, because the movie is set up to make us believe it. She might speak some truths, but she's not treated as a person in the movie, she's not a character in her own right, and our lasting impression of her isn't that she confronted Tony with the truth, but that she's a hypocrite and shallow and not the right type of female character (which Pepper Potts clearly is).
And what kind of character is Pepper Potts? She's clearly set up to be a highly capable, highly intelligent woman, stylish, demurely attractive, someone that Tony Stark simply could not live without. And her actions are important to the plot. Her joking plaque of Tony Stark's heart saves his life when his second arc reactor is stolen. She shows that she has nerves of steel when she faces down the villain and escapes with proof of his actions. And she's the one to push the button that ultimately takes the villain down. So she's a hero, yes? A highly capable female character who's not a damsel in distress and doesn't need Tony to survive.
Except she's not. Because Pepper Potts has no life or personality beyond Tony Stark. She talks about him in every scene she's in. We know nothing about her life beyond him -- where she lives, her other friends or relatives, what her hobbies are, how she feels about her entire life apparently being dominated by a really selfish billionaire. She has "plans" on her birthday, which he disapproves of, but we don't know what those plans are. She doesn't exist beyond him.
And, apart from one jokey plaque, she doesn't take much initiative beyond her role as a personal assistant either. She might do important things like press buttons and remove dangerous wires, but she only does so after Tony asks her to. She is literally just his assistant, an extension of him, performing whatever tasks he is unable or unwilling to do.
But hey, the movie tried. No woman dies to advance Tony's emotional arc. Pepper Potts doesn't get kidnapped. She has scenes all to herself. She talks to another (eventually) named female character. And that's better than a lot of superhero movies manage.
So is this half-hearted effort better or worse than a movie that just doesn't seem to care? I'm not sure. It's frustrating to watch at times, but it does bode well for the potential of the superhero movies to follow, if only the writers put in some effort. The storytelling and other elements of a good movie are there. The female characters are waiting in the background. They just need someone to bother to bring them together.