Robert Downey Jr. kept food hidden all over the lab set, and apparently nobody could find where it was, so they just let him continue doing it. In the movie, that's his actual food he's offering, and when he was eating, it wasn't scripted, he was just hungry.
In the final end credit scene, Captain America is the only one not eating. That is because Chris Evans got a buzz cut, and grew out his beard after this movie was done filming. He was called in later to do this extra scene, and couldn't shave off his beard, due to filming Snowpiercer (2013) at the time, so they gave him a prosthetic jaw. He holds his hand over his face because the prosthetic made him look like he'd been attacked by a hive of angry bees. He also is unable to eat or talk with the prosthetic on.
There were very few times that everyone was in town at once, but on one night when they were, Chris Evans sent them all a text message reading "Assemble" (the tagline to the movie), prompting a night out on the town. Clark Gregg has stated that this is his favorite text message that he has ever received.
Director Joss Whedon encouraged improvisation on set. Reportedly, Iron Man's "Let's just not come in tomorrow" speech was improvised by Robert Downey Jr., as was Tony's remark that his arc reactor is a "terrible privilege". Whedon also suggested "Shakespeare in the park" to Downey Jr., who then added the line "Doth mother know you wear-eth her drapes?" himself.
Reportedly, a scene was filmed where, during the final battle, Captain America saves an old man trying to protect his grandchildren. He tells him to "Get them to cover", but as he walks away, the old man asks him "Cap, is that really you?" He turns and, noting the man's World War II veteran lapel pin, trades salutes with him. As Captain America sprints away, the children ask their grandfather, "Do you know him?", and he replies "we all know him."
Stan Lee: (at around 2h 10 mins) Creator of such Marvel comics as the X-Men, Spider-Man, the Incredible Hulk, the Fantastic Four, Iron Man, Thor, and many others, is the old man being interviewed at the end of the New York battle montage who says: "Superheroes in New York? Give me a break!" and then returns to a game of chess with a fellow senior citizen. He also appeared in a deleted scene: after witnessing a waitress flirt with Steve Rogers, Lee's character says, "Ask for her number, you moron!"
Harry Dean Stanton: Janitor who encounters Bruce Banner after Hulk falls out of the Hellicarrier and crashes into a building.