There were actually many references to the original film. I watched the Charlton Heston version immediately before seeing RotPotA and I was amused to see some of the subtler points integrated. On the other hand there were some points that were unfaithful to the original. I never saw the 2001 remake of Planet of the Apes so this may have been explained away in that, but the voyage that the Heston character was on was supposed to be into "deep space" not to "Mars"...
And apart from the connections to the original film, I must say that I wasn't that impressed... The film took itself too seriously and because of that its lack of believability was a lot less forgivable. The apes were anthropomorphed to a ridiculous degree that detracted from the film. It would have been much more effective if they'd made the apes intelligent but hadn't used human culture as the touchstone of intelligence. Why was it important that the apes should take on human morality and concepts like honor? Intelligence with a different standard of behaviour - now that would have been much more realistic and in a way terrifying in the same sense that aliens are terrifying.
And the final point I have to include to be fair. The theater was filled with talkers when I went. I've never seen such an obnoxious crowd. There were probably 5 different groups of people who spent the entire movie cracking wise and trying to outdo each other by shouting out one-liners of their own devising. It was maddening. That probably effected my consideration of the film.
rise of the planet of the apes