During the congratulatory dinner early in the movie, the food on top of Charlie's head changes between shots.
As Richmond and Lyrae talk at the telescope overlooking the bay, the wind is causing Richmond's unbuttoned suit coat to billow quite a bit. As he turns to his left, and a new shot begins, his coat is suddenly buttoned.
When Capt. Richmond Talbot asks Lyrae where she is from, she says that she is from Betalyrae. She adds that "it is planet beyond the star that you call Andromeda". But no one would call Andromeda a star; Andromeda is a galaxy consisting of billions of stars.