Anakin cuts off one of the IG-86 assassin droid's arms. When the assassin droids jump up into the rafters they both have two arms again. The droid fighting Ahsoka has two arms as it jumps down, but on landing it has only one.
When Anakin tells R3-S6 that he'd make a poor excuse for a light-switch, the droid's dome appears reversed (flipped shot).
Ahsoka introduces the new R3 unit to Anakin as the "newest" model of astromech droids. However, in Star Wars Episode II: Attack of the Clones, Obi-Wan uses an R4 unit on his missions to Kamino and Geonosis which takes place before the events of this episode.
Rex's Kama (his skirt) disappears twice: first when he and Ahsoka are looking at a hologram of an AT-TE that Anakin pulled up, and then later when he orders the AT-TEs on the asteroids to fire.
Just before Anakin lands his starfighter inside the Twilight, his hair is parted on the wrong side (flipped shot).
In the first shot when the Twilight is flying through the debris field over Bothawui, the wreckage of an Acclamator-class assault ship can be seen in the background, even though no ship of that model participated in the battle.
The other members of his battalion are able to retrieve Anakin after his crash without also retrieving his ship or R2-D2. The only way this could be possible is if he was somehow ejected a very long distance from the ship, but if that happened, the vacuum of space would kill him before he could be rescued.