In the vision sequence when Loki projects himself to The Other, The Other says "The Chitauri grow restless" and his face is seen unmoving. When speaking his next line in the same shot, his face is clearly animated.
When the helicarrier starts to go down, Nick Fury tells Iron Man, "Stark, we're losing altitude," and display inside Iron Man's faceplate is counting down from about 15,000 feet. A few minutes later when Fury glances at a display on the bridge, it is counting down from 18,000 feet.
In the gym, Steve Rogers starts removing the wraps from his right hand and holding them with his left. When they switch to the shot over his shoulder, the hands have switched wraps. In the next shot they're switched again.
During the final battle, Iron Man explodes a "Leviathan" - one of the big Chitauri monsters - from the inside, labeling his attack 'Jonah-style'. He falls and hits a cab, which stops him. The camera angle then changes, and the cab is nowhere to be seen.
When Capt. America is in the gym punching the second bag, the bag has no tape around the middle. When he and Fury begin talking, a close up of the bag has duct tape around the center. Next it switches back to clean again.
The number of soldiers accompanying Hawkeye during his attack on the Helicarrier is inconsistent. We see 7 soldiers with Hawkeye when they enter through the grate on the deck, however we see a total of 8 during the subsequent scenes. 2 are killed by Nick Fury and 1 by Maria Hill in the initial shooting on the bridge. We then see another 3 at the damaged engine fighting Captain America (he knocks one out and throws another off the ship - the final one is knocked out by Iron Man). Another soldier is shot by Fury in a subsequent bridge scene and finally the 8th is subdued by Coulson in the detention area.
After Captain America stops Iron Man and Thor from fighting, Thor knocks Iron Man behind him a good distance before hitting Cap's shield. But when the dust settles not only does Iron Man wake up pretty much next to Cap, he is also in front of Thor somehow.
The plane with Captain Rogers and Agent Phil Coulson lands on the carrier you see a crew member in an orange shirt directing the plane on where to land, he is close to the plane, when the shot changes to an overhead shot he is not near the plane.
When Nick Fury is talking to Steve Rogers in the gym we see Steve from in front removing the bandage from his right hand, when the scene cuts to Steve from behind he is removing the bandage from his left hand, when it cuts back to the front view he is removing the right hand bandage again.
Agent Phil comes to the Stark Tower to meet Tony. Pepper hands him her glass of champagne. During Pepper's conversation with Agent Phil, he holds the glass by the bowl, but in one shot he is holding it by the stem.
The reception scene said to take place in Stuttgart, Germany, was clearly filmed in the U.S. (Cleveland, in fact) There are no such skyscraper buildings in Stuttgart as seen in the background. All S-Class Mercedeses shown are U.S.-spec-models, easily recognizable by the yellow front side marker lights. Furthermore, Königstrasse is mainly a shopping street, and Königstrasse 22, in particular, is a shopping arcade containing, among a dozen shops, two cinemas. There is no building in the vicinity higher than half a dozen floors, and Königstrasse 22 opens on the street, not on a square. Furthermore, Stuttgart has no elevated trains, which can be seen in the background of the square scene.
In the very beginning of the movie, when Black Widow is being interrogated, the exterior shots shows a billboard with supposed Russian writing. However, the actual writing makes no sense and is just a collection of random Cyrillic letters. Additionally, the locomotives of the train seen passing by are all new American mainline freight locomotives, and would never be used in Russia or Eastern Europe in general.
The German police shown in the Stuttgart-scene have yellow light bars. In reality all German emergency vehicles have blue flashing lights. Yellow flashing lights are reserved for roadside assistance and construction machinery.
When the computer locates the Tesseract's location while the Avengers are arguing with Nick Fury, the computer displays the location with Latitude & Longitude coordinates that doesn't conform to the format it's displayed in. "LAT:45°66.12 'N /LON:76°87.32'W" is shown, the format is degrees & minutes. The minutes must be between 1 to 59, here we can see 66.12 and 87.32 are greater than 59 and not a valid way to display minutes in this format.
S.H.I.E.L.D. Quinjets flying at night are shown with red navigation lights on each wingtip. There should be a green light on the right (starboard) wing, and a red one on the left (port) wing. These are known as Right-of-Way lights, and follow the same rules that were established for watercraft in the mid-1800s.
In the end-credits scene, the Shawarma restaurant is indicated by signs, t-shirts, and a chalkboard with shawarma, kabob and vegetarian specials listed. However, the back-lit menu at the top clearly shows steak, sandwiches, soups, Thai chicken salad (among others) and onion rings, and no indication of shawarma, gyros or other middle eastern/Mediterranean fare.
During the fight between Natasha Romanoff and Georgi Luchkov (Jerzy Skolimowski) Luchkov's hair changes length and whiteness between shots revealing an obvious stunt double in place of Skolimowski during the more physically-demanding shots.
Where the little girl in Kolkata searches for Dr. Banner, the Bangla signboards have typographical errors: 'Chemist' was written in Bangla like 'ka-me-sit', 'Watch Service' appeared as 'ghardir da-o-kan. Even 'Centre' was partially seen to be written as 'ka-ne...'.
This most possibly occurred due to transliteration from english to Bangla unicode.