When Lizzie attempts to confess to Kate in the hallway she is wearing a red and white shirt with no bag. However in one shot from behind, you can see that there is a blue bag strap over her left shoulder. This is the same blue bag she can be seen wearing in later scenes.
When Lizzie, Miranda and Gordo enter the cinema to watch "Vesuvius: The Eruption" if you looks closely at the poster for the movie behind them, you can see it has "A Stan Rogow Film" printed near the bottom. Stan Rogow is an executive producer of the show Lizzie McGuire.