Theodore Rex's shoes change from red to blue and back throughout the movie.
When the Guy in a Bag calls out to the caterpillar, it rises up. The puppet operator's hand is clearly visible in the first shot, lifting it from underneath the table.
When Katie talks to Theodore about his breath, it's a very obvious voice-over that doesn't fit at all.
After Ted is shot in his left arm, Katie tries to convince him he doesn't need a gun. As she does, the position of the gun changes between front and rear shots. Katie sways slightly in rear shots, but is motionless in front shots.