Near the end of the movie, when the Enterprise destroys the Klingon Bird of Prey watch the explosion footage. If you compare that footage to the footage of the exploding Bird of Prey in Star Trek VI The Undiscovered Country, you will find them to be exact. Guess the budget did not allow for another Bird of Prey blow up model.
Re-using footage is not necessarily a slip-up. What it is, is a movie studio not appropriating a large enough budget to shoot the entire film thus corners are cut and sacrifices are made.