In some scenes the Union Flag of Great Britain and Ireland is displayed, although this flag was not created until 1801 (nearly 200 years after the movie is set). In other scenes, St. Patrick's cross is omitted.
John tells Thomas to aim his musket with "both eyes open" which is actually a bad way to aim a gun as it's hard to line up your sights. However, firearms did not have rifling along the barrel back then, and even if you did aim perfectly with a smoothbore gun the bullet could still spin off path and easily miss a target less than 20 feet away. The fact that Thomas hit anything he was aiming at can be attributed only to luck.
Ratcliffe's maps show the island of Hispaniola (today divided between Haiti and the Dominican Republic) underneath Florida, where Cuba should be. Although 17th century maps are known to be inaccurate, a mistake this obvious is unlikely given that the Caribbean area was well charted by then.
When John Smith first meets Pocahontas he is hiding behind a waterfall. He jumps through the water and levels his musket at her. His musket is a "matchlock" gun that is fired by having the "match", a chemically treated cord that smolders slowly, drop into the pan which contains gunpowder. If he came through the waterfall the water would wash the powder out of the pan and extinguish the smoldering match.
Pocahontas descends for 8.5 seconds before diving into the river, meaning she fell from a height of over a thousand feet and so hit the water moving at hundreds of miles per hour. Rather than emerging unscathed, she'd be instantly killed since the water can't get out the way fast enough, completely shattering her entire body.
Thomas falls overboard and is rescued by Captain John Smith. As the other sailors haul on the rope, both men sink deep down beneath the stern, but the ship is still moving forwards so the drag of the water would keep them on the surface.
A stable river will only divide into two streams if they're on the same level, such as in an estuary delta or passing both sides of an island. Pocahontas rejects the smoother course to take the right-hand stream which is a steep cascade - and that's what the whole river would've done long ago, draining the higher left-hand channel.
When John Smith sees the reflection of Pocahontas in water cupped in his hands ( when they first meet at the waterfall), the water would actually reflect the sky not the cliff where Pocahontas was hiding several feet behind and above him.
When the Native Americans are preparing for the battle, they are surrounding a big fire. Before they move to start the battle, they are all walking towards the center of the circle. As they do this everyone's shadow is right in front of them, as if the sun was behind all of them. This isn't possible since at least half of their shadows would be behind them and not in front of them.