The opening scene can really hit home for people who have had to take care of their dying parent and that itself is another tearjerker.
Subtle Bilingual Bonus with Ivan at the start of the scene. Anton calls his name a few times. Ivan ignores him. Anton uses Ivan's diminutive name (the one more associated with his youth): Vanya. Ivan pays attention.
A FridgeTearjerker when Tony is in his Iron Man suit, munching on a donut, sitting in a giant donut, wearing shades. Although this scene is Played for Laughs, when you subtract the amusing background music used in the scene and the inherently funny nature of Iron Man sitting inside a donut, this is a really depressing scene. He had just gotten into a fight with Rhodey, whose response was to take his Mark II suit to the Air Force, trashing both their friendship and Tony's desire to keep his tech private. His palladium poisoning was getting critical, leaving him with mere days to live (less than 72 hours, according to the tie-in comics), especially if he kept on accelerating it by using his armor. And after an attempted night of over-the-top partying was crashed by his best friend, Tony was so desperate to spend the last days of his life enjoying himself in new ways that he was reduced to sitting there on top of a donut store while wearing his armor and eating some donuts. Good thing Nick Fury showed up.
The fight between Rhodey and Tony. It's pretty badass at first, but then they start talking to each other. Take it from each end. Rhodey is desperately trying to save his friend from self-destruction, while Tony is coping (terribly) with the certainty of his death.
It's brought up in such a way that we're meant to find funny, but the revelation that Tony is giving away priceless belongings to charities. In addition to his increasingly reckless behavior, it's classic suicide warning behavior from somebody who expects to die soon, and because of how emotionally isolated he usually is, nobody (except Nick Fury) picks up on it.