Continuity mistake: When Hawkeye is breaking onto the Helicarrier, he and some snipers break down a duct cover and enter. When the cover lands on the floor, it is resting away from some pipes with some slats missing. As soon as Hawkeye enters the duct, the cover is now resting against the pipes, and the slats have reappeared.
Continuity mistake: When Steve and Coulson land on the Helicarrier, you can see two wings on the edge of the Quinjet they were in and they are both closed up. Next shot, as Romanoff approaches the Quinjet and Steve and Coulson exit, we can see one of the wings is completely open.
Continuity mistake: When Captain America, Black Widow and Hawkeye are fighting their way through the Chitauri in the S.H.I.E.L.D. jet, one shot shows the Chitauri blasting at the jet causing part of the front of one side to get blasted and a burn mark is left on the jet. A few seconds later, Loki blasts one of the engines and the burn mark on the front of the jet has vanished.
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.
Continuity mistake: Right after the second engine goes down on the shield Helicarrier, the altitude reading on Iron Man's HUD shows just over 15,000 feet for the altitude. A short time later, even though the helicarrier has been falling since the engine went down, the altitude on the helicarrier's bridge shows the helicarrier falling through 18,000 feet.
Continuity mistake: After the Chitauri have arrived, Loki stands on the Stark Tower balcony and looks on New York. In this shot, Loki is standing facing the city directly, but by the next shot, he's suddenly standing 90° in the other direction with his head turned to the right, in order to be looking the same way as in the previous shot.
Factual error: During the scene on the Helicarrier where Bruce Banner "Hulks out" and jumps at the F-35B hovering just outside, we see the F-35B fire its guns, one inside each of its intakes. The F-35B has only one gun, externally mounted to underside of the fuselage. It would be impossible to mount a gun inside an aircraft's intakes.
Other mistake: What special "something" does Nick Fury use to pick the Cosmic Cube up at the beginning of the movie? All I saw was that he had on a glove, but in Captain America it was said only people with special abilities could handle it, and even later in the The Avengers when Banner is moving the cube, he uses a gadget and he's the Hulk! Did I miss something?