Other mistake: Just after Grandma Willow says "There's still some snap in these old vines," John Smith puts on his bag, but he just presses it to him instead of putting it over his head.
Other mistake: When Percy sees Meeko in the bubble, it is done in first person perspective and we can see straight through the bubble, showing that Meeko is not there on the other side.
Answer: This is a question the movie chose not to answer. It could be assumed he died as the Powhatans did not have the knowledge to treat gunshot wounds. However, there were cases even as far back as this time of individuals being able to survive gunshot wounds as long as the bleeding could be stopped and infection didn't spread. As the Powhatans did know herbs in the land to treat infections and did know how to mend bleeding; it is also possible he lived though he would have walked with a limp for the rest of his life.