Plot hole: While it is essential to the story, there is a problem with apes in the space ship. While it is the one that took Taylor to the future, there is no way the chimps could have salvaged the ship from the water (plus there wasn't enough time for such a salvage operation. Kira and Cornelius were living in the ape city we see in "Beneath the Planet of the Apes" never mentioning to Brent that they found a spaceship he could travel back with). They didn't have the technology for such an operation, no diving suits, and chimps are scared of water. Also, the water would have destroyed the power systems of the ship when it sank. (00:00:25)
Plot hole: It doesn't make sense that Mary is English with a heavy English accent, while both her brother and father are obviously 'Aussies'. Even if she was adopted to an Australian family, she wouldn't claim to be English, she would be a naturalised Australian.
Plot hole: When Harry is on the roof of the first shooting, he finds the spent shell casing. Later in the office he says that they think it is a 30-06. He has the shell casing. He *knows* if it is a 30-06 or not.