The movie, which purports to show the collapse of the Maya, ends with the appearance of the conquistadors. The collapse of the Mayan civilization (through famine, deforestation, drought, and the collapse of center city happened in the year 900, at a time when the Spanish (who would not send explorers to the New World until the late 1400s) were under an Islamic caliphate. It is totally impossible that conquistadors would appear during the Mayan collapse (unless time travel).
(at around 1h 9 mins) The murals in the tunnel are nearly exact replicas of murals dating from 100 BCE, 1,700 years before the movie is set. However, the real murals don't show people brandishing bleeding, severed heads.
(at around 58 mins) As the captives approach the Mayan city, they come across a girl and her dead mother. Both of them show clear signs of smallpox, particularly the blisters on their face. However, smallpox is a disease brought to the New World by the Europeans and, since the film takes place before the arrival of the Spanish, it's impossible for them to have contacted the smallpox virus.
The style of sacrifice portrayed in this movie are Aztec in style e.g. taking out peoples hearts and throwing the bodies down the temple, in the Mayan culture at this time they would sacrifice through decapitation.
(at around 48 mins) At the beginning of the scene where one of the (wounded) captives belonging to Jaguar Paw's tribe is thrown into the canyon, 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 around 1h 40 mins) When Jaguar Paw is in the trees and sees the torch lights of the hunting party, the close up shows his labret (lip) piercing missing. When he turns around, the piercing is back again.
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.
(at around 1h 16 mins) 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.
(at around 2h) 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.
(at around 1h 13 mins) 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.
(at around 1h 55 mins) 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.
(at around 1h 45 mins) When Jaguar Paw jumps from the waterfall and emerges from the water, his wound disappears. This has been fixed on the DVD; the blood has washed off, but the wound clearly remains.
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.
(at around 2h 5 mins) At the end of the movie, 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. Four seconds later he's looking straight into camera on his right. Watch the whites of his eyes.
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. Apocalypto shows Mayan culture, not Aztec, during this time period Spain was ruled by Muslims, and this Mayan civilization disappeared long before the arrival of European ships.
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.
(at around 1h 35 mins) 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.
(at around 2h 5 mins) When the Spaniards arrive, rain is pouring down on Jaguar Paw and his two pursuers. Yet the Spaniards' boats have 3 different pennants, all flapping gracefully in the breeze, with no water on them.
(at around 2h) 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.
(at around 1h 21 mins) 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.