Deliberate mistake: In "Dial Z For Zombies", Homer is shooting zombies with the shotgun at the school. When he shoots the first two he just shoots them twice. Every other zombie he shoots requires him to slide the gun. It doesn't when he shoots the first couple of zombies.
Plot hole: At the theatre in the "King Homer" bit, the audience are treated to a traditional showgirl spectacle. But the girls have no curtain behind them, and so the audience should have seen Homer the ape, but they act completely surprised a minute later when Homer comes on.