Plot hole: When the group are watching the brainwashing video, you can see Burns in the audience. Why is he there? He wasn't brainwashed with the rest of the group as we saw later in the episode. Later, he just disappears from the front row.
Continuity mistake: When Bart and Lisa are in the compound, just before Bart gets brainwashed, the bags that were behind Lisa disappear. Homer and Marge were on the other side of the room, so they couldn't have picked them up.