Ass Pull: Tony and Whitney suddenly dating. Ask any watcher of the show and they will admit they didn't see this coming. However this explicitly came just after this happened in the previous episode. So most believe this was just something to prolong the Unresolved Sexual Tension between Tony and Pepper.
To some extent, the same can be said of the show itself; half of the fans hate it for making Tony a teenager and other drastic changes to the character and his universe, while other love it for its good plot, character development, and use of various elements from the comic (such as the Armor War, Iron Monger or Extremis).
Complete Monster: Justin Hammer is a youngweapons manufacturer whose company Hammer Multinational is the main competitor to Stark International. Hammer hires the super villain known as Mr. Fix to work for him and later injects Fix with a nano virus, that will kill him if he disobeys Hammer. After Iron Man defeats Hammer's Titanium Man armor, Hammer blames Fix for the armor's failure and uses the nano virus to kill Fix's body, but uploads his mind into Hammer's computer systems, much to Fix's dismay. After Stark International lands a big military contract, Hammer decides to get revenge by placing a control device on Stane's Iron Monger armor and sends Iron Monger on a rampage. After receiving blackmail messages from an unknown party (actually sent by Mr. Fix.), Hammer becomes increasing paranoid and Ax-Crazy. Hammer starts attacking anyone who he thinks may be responsible, including his own men. Hammer uses a new chemical weapon called Z Gas to turn crime boss Count Nefaria into a zombie and then kidnaps and tortures Killer Shrike, one of his former henchmen. Hammer then turns Shrike into a zombie. After Iron Man broadcasts evidence of Hammer's crimes across the globe, Hammer starts to lose it and plans to release the Z Gas on New York City.
Damsel Scrappy: Pepper Potts has two purposes for her existence: help Tony out on occasion and get captured and rescued constantly even in situations she should be able to escape from on her own. Her behavior is consistently damsel-like despite her aspirations to be a kick-ass SHIELD agent - at one point she's in the middle of an abandoned warehouse where two different factions of Chinese assassins are fighting and she sits there waiting to be rescued instead of getting away from the fighting. Yeah, real SHIELD material.
Rescued from the Damsel Scrappy Heap: She finally gets her armor to fight with in the three-part season 2 finale. She even gives herself the name Rescue since she just rescued Tony and Rhodey multiple times since getting it.
In Hawkeye's first guest appearance, Iron Man hits him with sonic blasters, causing Hawkeye to protest that he has sensitive ears. The comic-book version of Hawkeye has since been retconned as hearing-impaired.
In the episode "Dragon Seed", When Pepper takes her new armor out for a test drive, Rhodey says something along the lines of "Let's hope she doesn't take out New Jersey." Tony replies, "Let's hope it'sthe shore." Well, thanks to Hurricane Sandy....
Xin Zhang is heavily implied to have murdered his wife.
Subverted with Gene when it's revealed he caused Howard Stark's accident, but it turns out he didn't kill Howard and kept him alive for information. Of course, from Tony's perspective, it's still played straight. Not to mention the fact Gene was going to kill Tony that day because he didn't see any use in him, it was only thanks to his armor that Tony survived.
Never Live It Down: Pepper isn't really as useless as much as her detractors like to make out. While she is the go-to Damsel in Distress, she's rarely the only person at the time in danger, and while not an Action Girl, she does have her own contributions to the team (notably, she was once able to track down the wife of the Crimson Dynamo's pilot, in order to get him to stop his rampage, using nothing but detective work and pretending to be an FBI agent). However, the Damsel in Distress aspect of her character has made people ignore her other aspects and write her off as The Load. Though it doesn't help that Pepper herself seems to see herself as The Load and hoping to get her own armor to stop being that.
Periphery Demographic: Despite being aimed primarily at boys, the show has an interesting amount of female viewers, which is usually unheard of for a superhero show. The show also attracts quite a bit of anime fans. Both of these are probably attributed to the show's heavy anime-influence as well as it's effort to not rehash the stories found in the comic books like other superhero shows, which have a history of alienating both of these demographics.
Special Effect Failure: A minor instance. In the second season, Pepper complains about Tony having gone without a shave in a while, making it look like he's growing a goatee. While this is presumably meant as a Mythology Gag, Tony's character model hasn't actually been changed to reflect it, so Pepper's comment comes off as rather odd.
Banner's transformation into the Hulk in this show (he just transforms in a flash of light and his clothes are back to normal when he turns back to normal) can also seem pretty lazy compared to the usual transformation sequences given to the character.
Tear Jerker: The ending of "Best Served Cold" will make anyone's heart clench.
Or the ending of "Designed Only For Chaos" for that matter.