Because I only love the original Planet of the Apes, I suddenly have this insane notion of having just the first Heston film existing alongside this series. I'll have to watch it again to see if there's anything mentioned in it that's contradictory to this series.
The entire portrayal of ape behavior is contradictory. The movie got the behavior of all three ape species completely backward -- chimps as the pacifists when they're actually the most violent great apes (or tied with humans), gorillas as the soldiers when they're actually the gentlest great apes unless provoked, orangs as the social and political leaders when they're the least social great apes. The new movies portray ape behavior much more accurately, thanks to scientific advances in the ensuing decades. Plus there's the fact that, y'know, they actually look like real chimps, gorillas, and orangs instead of humans in ape makeup that only broadly approximates the different species.
Oh, and there's the fact that the cataclysm in the original was nuclear rather than biological.