Continuity: When Zira is being interrogated, she says that the planet was destroyed in 3953 or something. The interrogator, later tells the President that the Earth was destroyed in 3955. In the original Planet Of The Apes, the ships display at the beginning of the movie shows that Taylor and his men crash landed in the year 3978. This would have been over 20 years later. Yet the planet was blown up in Beneath The Planet of the Apes at the end of the movie. So the timeline is impossible.

Revealing: Throughout the film, when the camera goes close to Zira, you can see the line where her wig is glued on.