Revealing mistake: You can see the blue screens on Bruce Banner's glasses when Tony Stark is talking to him about embracing the Hulk rather than disliking it. (00:57:40)
Revealing mistake: In the scene where Natasha Romanoff does a flip while tied to the chair, you can see her stunt double at the very end of her flip. Her arms become much more muscular. (00:14:30)
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. (01:43:15)
Revealing mistake: During the climactic battle towards the end of the film, when Hawkeye fires his arrow and rappels through a window, the camera pulls in close to him. Watch as he begins to roll over: He rolls over a piece of glass, which smushes up like jello under his elbow. It's obviously a piece of stage-glass. (01:57:30)
Revealing mistake: In the scene where Iron Man and Thor fight, Thor begins to crunch Iron Man's metal arms so Iron Man fires at Thor and then headbutts him. In the shot from behind Iron Man, part of the green screen is reflected on the right side of his helmet. Can't be a tree or a bush because those are all dark green colored and the reflection is much lighter. (00:46:55)
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.
Answer: People have been smuggled in and out of countries for decades, grease the right palms and talk to certain people, if you don't get in under the radar, phony papers could.