Continuity

Theodore Rex's shoes change from red to blue and back throughout the movie.

Crew or equipment visible

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.

Audio/visual unsynchronised

When Katie talks to Theodore about his breath, it's a very obvious voice-over that doesn't fit at all.

Continuity

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.