A clear discontinuity when Joyce picks up the baby and returns the pillow in the cradle. It's obvious it's two separate shots.
Joyce trips over the candle near the end of the movie. At the next shot of the candle, candle is not burning.
When Joyce is hallucinating and sees a girl instead of a guy that brought the groceries, you can see a boom mic at the top of the screen. It can be seen later in the same scene.