In the middle of their flight, Marcus and Esca lose their beard stubble and are suddenly clean-shaven.
During the final chase scene, it is shown to be raining and yet the dried mud/paint of the Seal people remains pristine and unwashed away. This simply isn't possible.
When Marcos was honoring the dead body of his father's friend the captain, and set it on fire, a heavy smoke covered almost his face while praying (1:43:16) then when Marcos & Esca put the mascots there were no smoke at all.
When the Roman patrol is dispatched to look for the lost grain shipment, a signifier is seen leading them out. This is not factual. The signifier was the bearer of a Roman legion or smaller sub-unit's standard, eagle, or symbol of the emperor. A signifier would not have been part of a routine patrol.
Aquila, as leader of a detachment of at least cohort strength, would not be wearing a Centurion's helmet. His helmet would have a parallel crest, like his second in command. A Centurion is the equivalent to a Captain/Company Sergeant Major, where a Cohort commander would be equivalent to a Lt. Colonel.
Marcus noted that Esca knew the Northern language and could interpret. Esca was the son of a Brigantes chief and spoke Brythonic, which is close to Welsh. The Brigantes had controlled a large section of northern England. When they pass through Hadrian's Wall into Scotland, Esca speaks in Gaelic to everyone. There were no Gaelic speakers known to be in Scotland in 120 A.D. Most scholars believe the inhabitants [the Picts] spoke a Brythonic language related to but distinct from British. The first Roman recording of Gaelic speakers [the Scotti] in Scotland was in a skirmish at Hadrian's Wall in 297, and immigration wasn't until circa 400 A.D. Esca could indeed interpret, but in Brythonic not Gaelic.
Nearly all Roman soldiers are shown wearing crude leather vambraces. While the Roman army of that era indeed had a complex arm guard known as the manica, these were not standard issue, composed of metal plates, and considerably more sophisticated than the fairly basic pieces of equipment worn here. Furthermore, although vambraces similar to the ones from the movie were used in later Roman armies and by the Byzantines, there is no evidence to suggest that they were already in use in the 2nd century.
As Marcus and Esca ride across the countryside, they use stirrups, which were not known in Europe until the 7th century AD. This was due to potential insurance issues, especially as Jamie Bell hadn't ridden before this film.
As Marcus and Esca enter the village of the Seal People, there is a shot of the young boy looking up at them. To the left of him are a pair of legs of a man clearly wearing a pair of modern army boots.
The screams of a red-tailed hawk are used in place of eagle sounds. Red-tailed hawks do not live in Europe.
When Uncle Aquila tells him after being wounded he was transported 200 leagues for care is in error. Hadrian's wall was across the middle off Great Britain. A league is generally accepted to be equivalent to 3 miles so that would place him more than 100 miles south of Great Britain.
When Marcus and Esca pass Hadrian's Wall and head north, they are both pictured riding bay horses. Shortly thereafter, and for the rest of the film, they are seen mounted on war horses, 1 black, 1 white. No explanation of where they got these horses is forthcoming. (In the shooting script it is stated that they took these horses from the "rogue warriors" they killed, but in the actual film, the horses appear before the scene where they kill the rogue warriors.)