In episode 4 when Haruko pulls the Flying V out of Naota's head, you can see six tuning pegs on the headstock; in episode 6 when Naota strums a string on the same guitar, the sound is that of a bass guitar.
During the dinner conversation in episode 3, it was mentioned that Haruko ran over Ninamori with her Vespa. This was not accurate, Haruko fell off her bike, the bike continued on and hit Naota, who was then sent careening into Ninamori.
In the sequence within the beauty salon, Haruko uses a knife to stop the bullets that the agents are shooting to her. But when the bullets falls to the floor sliced in half, the bullets are still in their shells.
In the first appearance of Haruko her guitar case is around her back. Once she grabs her guitar, the case has completely disappeared. At the end of the scene her case appears on her back again with the guitar apparently inside.
In the under-the-bridge sequence in FLCLimax, two goofs are made regarding Mamimi's cigarette. When the small robot (terminal core) tries to take her cellular phone, she drops her cigarette. When she crouches on the balls of her feet, however, it can be seen that the cigarette is gone and not on the ground. After that, a cigarette appears in her mouth, lit and glowing... but in the next shot it isn't glowing any more.