1. When Dr. Aki Ross (the female scientist) and Capt. Gray Edwards (the army guy) are in the spaceship near the end of the movie, they float around the ship in micro (near-zero) gravity. However, Aki's long hair stays down neatly, while it should be flying all over the place.
2. When the Zeus weapon explodes in outer space, there is an audible bang. I realize this happens in all space movies, but it is an error. Sound waves can only propagate through matter; the near-vacuum of space should create complete silence.