Continuity mistake: Right after Aki saves Gray and turns around to pick up the canister containing the plant off a table there is no table or ledge. If you watch the movie with the commentary one of the members involved with the movie says that it is floating on nothing. (00:16:50)
Continuity mistake: When Aki gets cornered by phantoms in Old New York at the beginning of the film and the Deep Eyes come to rescue her, all four members of the Deep Eye Squad jump from the transport (even though one of them should be the pilot), but only three of them hit the ground. Just a few seconds later, Aki tries to escape through a gap between two buildings. The three Deep Eyes follow her. When Ryan shoots at two phantoms hitting some explosive tanks in one of the next shots, you can see four Deep Eyes again. (00:07:15)
Continuity mistake: When Gray is being operated on by Aki (he's on the medical table) you can clearly see a reddish-brown scar on the lower left side of his neck (it's not a recent wound). It appears off and on for the rest of the film. Example: you can not see it when they are conversing after escaping to space in her ship after everyone else dies.