When Athena confronts Achilles in his apartment to render him unconscious with an injector, it's all too easy to spot Athena pulling what is clearly a glue gun out of her outfit. This is then "matched" to a much better looking prop injector in an insert - followed by a cut back to the shot with the original glue gun.
During the first Achilles/Alexander fight, Achilles fires the "secret" green laser from the Robot's chest turret. However, it was stated very bluntly during the weapons briefing that the laser was mounted in the shoulder turret.
Achilles' scars change throughout the movie.
Achilles is supposed to be illiterate. This is referenced at least twice in the film; first when Commissioner Jameson reminds Achilles that he isn't even able to read his own contract (which Achilles acknowledges), and second when Achilles asked his brother how the "reading business" was going. However, after he comes out of retirement, Achilles questions Doc Matsumoto about the countdown sheet for his upcoming rematch against Alexander, which he has just read. If Achilles is in fact illiterate, then he would not be able to read the countdown sheet.
When Athena enters the robot, she has on a dark visor. This is supposed to protect her from the new flash weapon and helps her get in the robot without being suspected that she is not Achilles. She is knocked down unconscious in the fight, and Achilles comes to rescue her and fight in the robot himself. When he puts on the suit, the visor is now clear for the rest of the fight, as it was for all of his "in the robot" scenes.
When Athena confronts Achilles in his room and sedates him, in the ensuing fight when Athena sweeps his leg and then spins around with a flying kick, you can plainly see that it is a stuntman.
It is never explained why the tranquilizer given to Achilles by Athena never has any effect.