"Explain how everyone survived the NUCLEAR EXPLOSION that Leo triggered on the Oberon to defeat the apes INCLUDING the apes right in front of the explosion!
Explain how the apes in the couple of thousand years since Pericles’ time got so much taller."
What makes you think the explosion was nuclear? Although I agree that the movie suddenly got lame when the apes who had just been blasted 100 yards into the air are merely “groggy” after they crash back down to the ground.
As for the other question, the log Mark Wahlberg finds indicates that the scientists on the Oberon used the apes to keep themselves alive for some time before the revolt. Evidently, in order to survive, they began much more aggressive genetic engineering, arriving at the apes we see in the film. This manipulation might have had other side effects, such as a drastically supressed birthrate, explaining why the humans were able to out-breed the apes.
As for all the other plot holes, all bets are off if a story involves time travel. Maybe in the year 10,500 a ship transporting horses to the Intergalactic Zoo hits the same storm and lands on POTA before anyone else gets there. Maybe Thade travels back in time and helps the South win the Civil War by giving them AK-47s. Maybe Thade is actually Wahlberg’s and Helena Bonham Carters descendent from the time they got it on .00005 seconds after the Big Bang.