These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Base Breaker: The brusque, collected Natasha Romanoff is easily the most understated major character in the either film when it comes to personality tics. Some fans liked this, finding her icy and enigmatic while others found her bland and lacking in personality. This is difficult to gauge considering Natasha spends the majority of her time undercover so she doesn't have much time to display her true personality.
An interview with the director revealed that the more flirtatious scenes between Natasha and Tony were cut to preserve the Tony/Pepper relationship. A scene from the first trailer even features Natasha smiling.
Critical Dissonance: Rotten Tomatoes scores designate this as one of the least well-received movies in the first phase of the Marvel Cinematic Universe, second only to The Incredible Hulk. Despite this, it became one of the highest-grossing movies in the phase, trailing only its predecessor and The Avengers.
The video footage of the Hammerdroid's test malfunction (twisting around so fast it snaps the pilot's spine) evokes a That's Gotta Hurt gasp of sympathy from the audience. But Hammer's mealy-mouthed attempts to gloss over the failure by insisting that the pilot survived cross it back into a joke at his expense is quite funnier, as is his later statement that people are reluctant to volunteer to test them "for some reason."
Also, Tony's birthday party. "Iron Man, how do you go to the bathroom in that suit? ...just like that." Not funny. Giving an actual technobabble answer about filtration and being able to drink that? Now it's funny.
Draco in Leather Pants / Germans Love David Hasselhoff: Judging by the internet, a significant portion of Russian viewers seems to be rooting for Ivan Vanko/Whiplash, despite his villainous status. Given that his behavior qualifies him as a Magnificent Bastard and he comes across as a much more credible and threatening villain than Justin Hammer, combined with some patriotism, this is no surprise. Not to mention that he sets out to avenge his ripped off father, a much more sympathetic goal than the other villains in the films. Of course, a lot of people ignore the fact that he attempted to kill Tony for something his father did before he was even born, murdered several racecar drivers at the Grand Prix, both Hammer's security guards, and both a prisoner and a guard while locked up, as well as shot up the Expo and left bomb-loaded drones strewn about.
Ear Worm: The Stark Expo theme, as played over the closing credits. Make way! Make way! Tomorrow's heading our way... And written by Richard Sherman, one of the masters of the earworm, having written "It's a Small World" and many other catchy Disney songs.
Epileptic Trees: There was one for a while, before previews for Thor came out, that the prisoner Vanko walks by that the camera lingers on for a second was Thor.
During Hammer's description of "the Ex-Wife" he mentions it has a "cyclotrimethylenetrinitramine RDX burst". That's the same term being said twice, one's the chemical name, the other's the acronym. In other words, Hammer is simply reciting the spec sheet, and doesn't have a clue how it's supposed to work. Quite a subtle way to foreshadow that the weapon isn't all it's hyped to be.
During that same scene, Hammer says that if the "Ex-Wife" were any smarter, it would write a book that made Ulysses look like it was written in crayon. Ulysses actually was written in crayon: James Joyce's eyesight was failing, so he used crayons and large sheets of paper to make it easier for him to write.
In one of the notebooks from his father Tony looks through, a drawing of a hypercube, also known as a "tesseract", can be seen, foreshadowing Howard's work with the Tesseract after the events of Captain America and that the arc reactor is based on his studies of it.
Hilarious in Hindsight: The Stinger where Thor's hammer is found. Viewers may assume that it's government presence that circling the area. As Thor reveals, it's just a bunch of macho dudes trying to pull out the hammer.
Howard Stark is an expy of Walt Disney himself. (guess who owns Marvel now?).
This blogger speculated in jest that Oracle CEO Larry Ellison is Iron Man in Real Life. This was in March 2008. Two years later, Ellison makes a cameo at Tony Stark's birthday party in Iron Man 2.
The Internet is riddled with comparisons between Tony's Senate hearing and Hank Rearden's trial in Atlas Shrugged. Iron Man 3 turns Jack Taggert into "J. Taggart" — Jim Taggart is the name of an antagonist in Atlas Shrugged.
The scene where Tony greets "Mr. Musk"—Elon Musk, CEO of both Tesla Motors and SpaceX, playing himself—and Tony comments about how "Those Merlin engines are fantastic." Back in 2008 when the movie was released, this was just an inside gag about some new technology buzz. Since then, the Merlin engine has become the basis of SpaceX's Falcon 9 and Falcon Heavy launch systems, which look likely to slash the cost of orbital insertions compared to conventional rockets, including contracts with the DOD and INTELSAT.
Bill O'Reilly, who makes a surprising cameo as himself, commenting on his show about Pepper Potts becoming CEO of Stark Industries. It's much like the segments on his show in real life, but the fact that he's in Iron Man 2 makes it hilarious.
The Suitcase Armor. It's used for just three minutes and has the living crap beaten out of it, but the activation was so cool that the armor was used on the DVD cover instead of the Mark VI upgrade. Elements of it were also adapted into the Mark VII of The Avengers.
Pandering to the Base: Some people accused the movie of setting up the greater Marvel Cinematic Universe more than its own, due to the greater presence of Call Forwards like Captain America's shield, a clip from The Incredible Hulk, Tony being evaluated for the Avengers, Black Widow, Nick Fury's return, and Thor's hammer being found.
However, Nick Fury doesn't appear until more than an hour in and even then his purpose is more to get Tony off of his ass and work than to convince him to join the Avengers. He even tells Tony that how annoyed he is Tony has become his problem to deal with when S.H.I.E.L.D. has more on its plate to handle.
Pandering also seems to be parodied when Coulson discovers an incomplete Captain America shield. Tony asks for it excitedly... and uses it to prop up his machine.
Sequelitis: General consensus seems to be that the second movie is still an entertaining film, if not exactly as fresh as the first one. It may help if you think of it as the second in a trilogy.
Strawman Has a Point: Senator Stern is an ass, and Hammer is an idiot, but both of them make a lot of valid points in the senate hearing. Tony is a loose cannon, his suit is a weapon (whether he likes the term or not) of the sort that would ordinarily be denied a private citizen, and he is acting totally independent of anyone who could review his actions or rein him in if he gets out of control. None of these things are remotely desirable traits in someone who is trying to be a one-man police for the whole world.
As it happens, he's only acting out because the job's killing him. Notably, SHIELD agrees with Stern and Hammer that while Iron Man is useful, Tony Stark is too unstable. They still call him in for Avengers, on the grounds that they've hit the Godzilla Threshold.