Deliberate mistake: Identical twins Beverly and Elliot have the exact same beauty mark on their faces, roughly on the smile line directly across from the right nostril. Identical twins don't share features like that.
Deux Amours - S1-E5
Continuity mistake: Daryl fights the walker on the ship after it kills the other prisoner. He gets backed into a corner and jumps off the boat just as the explosions are happening. The walker he was fighting disappears.