When the camera is far away from Akira's capsule, the nameplate is in katakana (a Japanese alphabet). When Tetsuo walks closer, it has mystically been translated to Romaji (English) characters.
Near the beginning of the film, in the street bar, the sign on the jukebox changes from "MASTAR" to "MASTER" between shots.
Kai's socks appear to change color a number of times throughout the film, often from shot to shot within the same scene.
When Kaneda and his crew are walking from school, Kaneda's shoes change color in the same shot.
The rank insignia on the Colonel's uniform changes from 2 stars to 3 stars in some shots.
The movie mentions Neo-Tokyo hosting the 2019 Olympics. This is not an Olympic year. In fact, the Olympics never host the games during odd-numbered years. Obviously the stadium was just being prepared for the Olympics the following year. The film acknowledges the Olympics are a year away.
After the unnamed man escorting Takashi uses himself as a shield to protect him, Takashi apparently has spots of blood on his head, but as he gets up we see that blood was on the pavement and overlapped Takashi's head due to an animation error.
When Yamagata yells to Kaneda during the terrorist bombing, his feet are not touching the ground.
When the Clown biker is thrown through the window of the diner in the opening chase scene, the stack order of the animation cels changes for a couple frames (look for the curtains in the background briefly appearing in front of the fallen table in the foreground).
Publicist is misspelled as "publisist" in the final credits.
In the Streamline dub, the Diner Patron's mouth keeps moving after he shouts "Hey Waiter!" but nothing else is heard.