During the final battle, Hawkeye's clothes change back and forth - his coat on/off between shots.
(at around 1h 9 mins) Tony's watch said that it was 12.10 when he axed the logs outside. Then the watch changes into 11.20 when he talked with Fury inside the barn.
(at around 29 mins) After all the Avengers have tried to lift Thor's hammer, Thor picks it up with a drink in his hand. In the next shot the drink is on the table.
When Sokovia rises it is over land in the mountains. During the fight scene it is suddenly over a large body of water. When it crashes it is back over land again.
(at around 1h 9 mins) When Laura asks Tony to fix the tractor, Clint is seen picking up his son and moving. During the next scene when Tony walks off towards the barn, Clint is shown picking up his son again.
As Sokovia is rising to over 18,000 feet, the temperature would have been dropping about 5.4 degrees (F) per thousand feet. The temperature would have dropped below zero, yet no one's breath is seen and no one is acting cold.
Dropping a lump of rock the size of a small city from a great height (even when assisted by the thrusters that were used to raise it up) would not nearly have as big an impact as that of a meteor from outer space. Meteors get their high energy on impact from their high speed (usually around 17 km/s). A lump of rock dropped from 20,000 feet and assisted by thrusters would not go faster than about 0.5 km/s. The energy of the impact would be 1100 times less than that of a meteor of the same mass.
Despite Sokovia being elevated to nearly twice as high as the limit where oxygen is required to assist in normal breathing, no one during any aspect of the film mentions this or is shown being affected by it. People continue to run and fight as they would if the city itself was at its "normal" altitude.
@1h25m in the movie the train goes off the end of the tracks and continues rolling along the ground, through a building, through vehicles for a whole 45 seconds of the movie. While this seems visually realistic, trains which run on rails do not function like a car with rubber tires. The momentum of the train was provided by electricity from above and when it went off the rails there was no power source remaining. There would be far too much friction and loss of momentum for the train to continue the way it did for 45 seconds.
(at around 30 mins) During the after party battle in the Avengers building, several of the non-powered Avengers (War Machine, Iron Man and Hawkeye) are shown undergoing impact that should have either severely injured or killed them. War Machine (Rhodes) is shown being thrown through a plate glass 15-20 feet away and then falling an additional 20-30 to a concrete deck below. Iron Man (Tony Stark) is shown landing on a concrete staircase in manner that demonstrated he didn't prepare for the fall beforehand. Both should have been seriously injured or even killed from their impacts and yet later are shown only having lacerations and bruises to show for their troubles.
(at around 28 mins) Mjölnir shifts very slightly as Steve Rogers (Captain America) first tries to pick it up. He should not be able to move it at all. Actually, the Mjölnir shifts very slightly as to signify that Captain America is the most worthy of all the Avengers to use it albeit not enough. As a matter of fact we see Thor's first expression of fear when the hammer shifts and his subsequent expression of relief when the Captain fails to lift the Mjölnir.
(at around 1h 35 mins) Before the final assault on Sokovia, Quicksilver runs into the police station and exclaims, "We're under attack! Clear the city!" However, when he sprints out, the heads of the two policemen sitting behind the counter turn very quickly to follow him, indicating that the clip was sped up and the actors turned their heads in normal time.
(at around 1h 22 mins) During Captain America and Ultron's battle when Natasha/Black Widow is riding a motorcycle, it is obvious that it's a stunt double. This is due to the fact that any time she is shown from the front when the bike is supposed to be moving, her hair isn't.
(at around 1h 3 mins) When Hawkeye and Laura are in the farmhouse bedroom talking about the Avengers needing him, Laura's reflection is visible on the framed picture closer to the viewer. Yet, the angle is impossible, revealing it was edited there, possibly to cover an unwanted cameraman or equipment in the reflection.
(at around 1h 21 mins) When Captain America is hanging onto the front of the truck while fighting Ultron, the driving robot smashes through the windshield. Captain America swings himself around the truck and the actor's harness can be seen momentarily.
Around 1:20, when Captain America and Ultron are fighting on the truck, C.A. is thrown to the truck front. He spins around the windshield toward the drivers side door. In slow motion, what appears to be an arrow is sticking out of his chest is actually the harness that allows him to perform this feat.
@1h41m Quicksilver is running around hitting all the Ultron robots which are supposed to be made out of a super strong metal called Vibranium (see Black Panther). He hits them at super speeds destroying them, but Quicksilver doesn't have the ability to take blunt impacts and would more likely destroy himself with the first hit.
At around 1H9M when Thor, Steve and Tony are walking and talking right before the scene ends Chris Evans moves a little so he doesn't walk into the camera.
Barton flies back to New York with Vision (in the Quinjet), leaving Captain America and the twins in Seoul. Yet shortly after Barton arrives in New York, C.A. and the twins show up at the Stark Tower. There is no way they could have arrived so quickly. Since Barton took the Quinjet, they would have had to fly commercial - which is an approximately 14 hour flight. Additionally, Barton would have had to make several refueling stops.
When the truck with the package is running towards the law enforcement, they pull out their weapons which appear to be snub-nose .38 which is not a weapon for any eastern European country for their law enforcement. If they had a handgun it would most likely be a Glock model.
Despite the Marvel franchise later claiming in its show WandaVision that Wanda first receives her nickname of The Scarlet Witch in that show, Elizabeth Olsen is listed in the end credits as Wanda Maximoff/Scarlet Witch.
When Captain America is hanging from the bridge by one arm and holding on to a woman he is rescuing with the other, at one point, he lets go of the bridge to grab her with both arms, but remains hanging in place.
(at around 1h 50 mins) When Thor says, "I'm running out of things to say," it appears he is saying different words.
The initial confrontation at Ulysses Klaue's base states it takes place along the 'African coast' and the ocean is clearly visible near the grounded ships. The action with the Hulk immediately moves to Johannesburg (the city skyline such as the Hillbrow Tower is clearly visible), however Johannesburg is well over 300 miles (500km) from the nearest coastline.
At the end of Iron-man 3, Tony Stark had retired from being Ironman. Even going as far as destroying all his armors. Yet, here is back in the suit, and all his armors are back too. No explanation given. His retirement is not even mentioned at all, that arc gets completely disregarded. Furthermore, the character behaves as if he had never retired from his superhero heroics in the first place. As such, all of Tony Stark's character development from Iron-man 3 is ignored.
(at around 43 mins) When confronted by the twins, Ulysses Klaue says that he is afraid of "Cuttlefish. "Deep sea fish, they make lights, disco lights to hypnotize their prey...." Although cuttlefish do go to depths of 2000ft, they stay mostly in shallow water where they hunt crabs and fish using camouflage to sneak up on their prey before paralyzing them with venom.
(at around 39 mins) When the twins are describing the events that caused their parent's deaths, and their subsequent rescue, they mention that the bomb was only a few feet from themselves, yet people in all other (non USA) countries would relay that information in metric units, aka "only a meter away".
Ultron uses the term "for god sakes" when Hulk jumps in to the ship, to pull him out and throw him down. Ultron would not use this term given its artificial intelligence and consciousness.