Continuity mistake: When Maria Hill is being attended to after she gets hurt, her earpiece is on the left side of her face. In the next shot she is talking to Nick Fury and her earpiece is on the right.
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: 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: 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.
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.
Revealing mistake: Near the end, Captain America is shown riding a motorcycle without a helmet. Although the movement of the background indicates he's traveling at a good speed, his hair doesn't move.
Continuity mistake: Coulson walks into Stark's office and hands Pepper the file on the Avengers, which she promptly passes on to Stark. In the front shot, she is holding the champagne glass down by her waist. Cut to the shot from the back and you can see the glass just above her right shoulder.
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.