Continuity mistake: After the big battle, Iron Man lies on the street when Capt. America, all dirty and messy, says "We won." Iron Man sighs in relief and rests his head on the pavement. A frame later, from a wide angle, his head is raised, plus Capt. America's face is clean and his hair is brushed.
Continuity mistake: When Tony arrives at Stark Tower, he and Pepper share a bottle of champagne. In the shot where he says "Next building is going to say Potts on the tower", Tony's champagne glass is in his hand and there's no sign of another glass several inches either side. In the next shot, Pepper's glass is suddenly 2 inches away.
Continuity mistake: After the Tesseract opens up the portal that Loki enters from, 4 SHIELD guards are seen slowly advancing on his position. On the left side of the device, two of them are moving. The one further behind walks over an area of the floor that is illuminated by some orange light. The shot cuts to his feet, and suddenly the floor is dark.
Continuity mistake: During the big battle against the Chitauri, Captain America is zapped with a blaster bolt. When Thor helps him to his feet we can see a significant amount of damage done to his suit, just below the star on the right hand side. But later on after Iron Man destroys the Chitauri ship with the nuke, the damage is completely gone.
Deliberate mistake: The Mark 7 takes 9 seconds to assemble - give or take. Judging by the view of the Chrysler Building, Stark Tower is about 300 meters high. Even if you wouldn't count the time it takes for the suit to catch up with Tony, 9 seconds is too long, he would hit the ground before the suit would fully assemble.
Revealing mistake: In the scene after the Chitauri army enters the atmosphere, they start shooting people in the ground and in the next shot if you see underneath the bridge there is a restaurant with people running around to avoid getting hurt. If you see there are two glasses of wine and some food plates sitting in a table firmly which does not even move despite the blast wave that was created from all the shooting in the ground near it.
Continuity mistake: In the beginning of the scene "Mountaintop Battle" while Loki and Thor argue, Iron Man flies into Thor, tossing him to the ground below. Thor's hair is messed up and dirty. The shot changes, and when it goes back to him, he is standing and his hair is clean and neatly combed.
Continuity mistake: In the scene where Loki escapes with Hawkeye and Agent Hill is chasing them, she does a 180° spin and ends up face to face with Loki's driver. She shoots through the glass and you can see the bullet hole, but during the rest of the scene, the hole is gone, or moved to the passenger side.