At the beginning of the scene where one of the (wounded) captives belonging to Jaguar Paw's tribe is thrown into the canyon (around the 47th minute) a Western Cattle Egret (Bubulcus ibis) can briefly be seen. Although naturally spreading throughout the Americas in the previous century (presumably from stragglers flying in from Africa) the first record of the Western Cattle Egret is from the Guianas in 1877. The species established permanently in the 1930's in that area. After spreading north, it established in Mayan country somewhere between the late 50's and early 60's.
At 2:01:30, all three characters are staring in the same direction. As the camera zooms in to Jaguar Paw, the character behind him on the right is clearly following the camera. By 2:01:33 he is looking straight into camera on his right. Watch the whites of his eyes.
During the attack on the village, Zero Wolf's son gets hurt on the right eye. His father does two blood pressure release cuts below and to the right of his eye. When Zero Wolf gives his son the knife, the cuts moved further up to the right of his eye. During the "shooting range" scene, when the son is "the finisher", the cuts moved to the right and the top of his eye.
When the High Priest pulls the first warrior's heart out, the first shot shows no blood on his hands. In the next shot, as he shows the heart to the crowd, his forearms are covered in blood almost to his elbow.
When there are three warriors remaining in pursuit of Jaguar Paw, Zero Wolf greatly outpaces the other two, but after Jaguar Paw pauses to peer into the pit where his wife and son are trapped, the next pursuer to appear is not Zero Wolf.
The long feathers on the Mayan priest's headdress are supposed to be Quetzal, a native Central American bird and endangered species. They are actually the tail feathers of Reeve's Pheasant (Syrmaticus reevesii), a native of China.
The diameter of the tube created with the leaf to shoot the blow-darts was far too large to propel a dart without feathers or cotton to block off the escaping force of breath. A dart alone would barely make it out of a tube of that size, as most of the breath would be wasted blowing right over the top of the dart.
There are piles of hundreds of corpses dead less than a month, just outside the city, and more piles of hundreds of freshly killed corpses inside the city itself. At no point in the life of the Maya, and definitely not in the 16th century when the film is set, would the surrounding jungle have been able to provide a population large enough to yield that many sacrifice victims.
We see a solar eclipse and that night the moon is in the sky. Given that the (new) moon was on the Sun-ward (daytime) side of the Earth and given that it takes 28 days to complete a full orbit of the Earth, the (full) moon could not have been in the night time sky within 24 hours.
Jaguar Paw creates poison darts (thorns plus poison from frog) and a blow pipe (rolled up leaf) BUT there are no flights on the darts. Consequently, there was no airtight seal. His breath would gone past the darts in the pipe.
During the sacrifice just before the eclipse, a pile of torsos and heads is just right of the bottom of the steps. After a few frames of body parts bouncing down the steps and being caught in the baskets, a view of the other side shows a direct mirror image, not a different pile of bodies.
The goof items below may give away important plot points.
At the end, Spanish ships arrive near Jaguar Paw's village. This is a bit of artistic license; the huge temples and mass sacrifice portrayed in the movie were long gone when Europeans came to the Mayan area of Mexico. Apocalypto shows Aztec culture, not Mayan, at the time of the Spanish conquest. Furthermore, Kukulcan is a Mayan god, not Aztec.
The buildings in the city co-mingle architectural styles from three separate Mayan civilizations: Tikal Classic Maya (800 CE), Puuc (c.1050 CE), and El Mirador, a Pre-Classic metropolis that existed around the year 1 CE. If they wanted to portray Aztecs, this was definitely not their architectural style. If they wanted to portray Mayans, those civilizations disappeared long before the arrival of European ships.
A jaguar brutally mauls the face of a warrior chasing Jaguar Paw. The other warriors kill the jaguar, and a few of them argue over who gets a dead warrior's belongings. As the winner tucks it into his waistband, the mauled warrior's face is miraculously untouched.
In Jaguar Paw's final strike against Hanging Moss, Jaguar Paw holds the weapon in his right hand as Hanging Moss falls. In the next shot, as Jaguar Paw steps forward over Hanging Moss' body, the weapon is suddenly in his left hand.
The partial part of a solar eclipse takes about hour and half, while the total part typically lasts few minutes. In this movie however, both parts seem very short and of the same length, and occur in a minute time frame between the sacrifice of the last captive, and an attempt to force the same fate to the main character. This discrepancy then results in a funny effect of the moon seemingly coming to stop during the total phase and resuming its absurdly fast movement after it.