Continuity mistake: The cart with the prison meals is carrying 5 trays the first time it is shown in close-up. Inside the cell though, Kai takes his from a pile of 6. (00:08:40)
Continuity mistake: Amuro is explaining to his cellmates the key of the Gundam's combat abilities. He is sitting on the floor with Kai, but as the angle changes, the back of the sofa in the background is at an height that would make sense only if they were sitting on a chair. (00:10:40)
Other mistake: Bright realises that the door is unlocked as he pounds on it. The sliding door opens just a little, and the power is off, so it is implied and shown initially that they can be moved by hand. However when they go out of the room and when they go free Sayla and the others, it looks like the door are opening by themselves, not slid open by hand. (00:12:30)
Continuity mistake: When Bright turns towards Captain Paolo Cassius to tell him about the success of their operation, his three-way front tuft of hair is curled one way, the opposite way in the close-up. (00:21:20)
Plot hole: White Base and the interior of Luna II withstand without a scratch the explosion of the thermonuclear reactor from the Magellan from just a few meters, while the blast literally vaporizes the Zaku far away from the entrance and threatens to damage the Musai, hundreds of meters away.