For instance, there's a great exterior visual of the apes leaping out of a building -- through glass windows -- by the dozen. In another impressively-staged shot, we see that the apes apparently believe the quickest way to their destination is to go through an office building, not around it. Again and again, the movie reveals how the apes operate on different principles of behavior, and how that behavior prevents law enforcement from responding effectively to the crisis. That the apes are "evolved" plays into the matter too, of course. The police don't expect the apes to pick up spears, use city buses as barricades, or deploy advanced battle tactics.
Another mystery regarding Caesar's origin: What does the birth mark on his chest mean? Is it present simply so the audience can recognize and differentiate Caesar more quickly and easily in the battle sequences? Or does it carry another, deeper meaning? Is it some kind of future-ape culture "brand" (in a caste system?) that was put on him by his real mother and father (whomever that may be)? I don't know, and I like that the movie doesn't tell us too much.
Many reviews have also made note of the TV newscast that reports the disappearance of the spaceship "Icarus" on a mission to Mars. At least unofficially, Icarus is the name of Taylor's spaceship from the original film, and it's disappearance suggests the time-dilation or Hasslein Curve that we're expecting. A sequel to this film could have that spaceship arriving on Earth in a thousand years and finding Caesar's progeny.