During the Streamline Pictures dub, Takashi tells Tetsuo that if and when he awakens Akira, "no one can stop us". This incorrectly implies that the espers want to cause destruction alongside Akira. This error does not apply to the Japanese version or the Pioneer dub, where Takashi says that no one will "stop him" (referring to Akira).
In the Streamline dub, one of the councilmen during the executive meeting states that the anti-government terrorists "tried to kidnap Number 25". It is clear that he is referring to Takashi, the esper who is abducted by the terrorists early in the film, but Takashi's designation is Number 26, not 25. (It may be possible that the councilman confused Takashi with the real Number 25, Kiyoko.) This does not occur in the Japanese version or the Pioneer dub, where he correctly refers to Takashi as "Number 26".
In a long shot of Nezu discussing Kaneda's usefulness to the resistance movement with Ryu, a passing-by couple appears to be walking towards the same set of steps that Nezu and Ryu are about to descend. However, in the next shot, the couple is walking up a flight of steps on the other side of Nezu and Ryu.
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. By coincidence, Tokyo will host the 2020 Olympic games, but they didn't know that in 1988.
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.