Continuity mistake: When Joe is leaving the dinner party after talking to the grief counselor, he puts on his jacket and the collar of his sweater is flat underneath it. The camera cuts away and when you see him again his collar is standing up closer to his neck. Then the camera cuts away and his collar is flat under his jacket when it comes back to him again.
Factual error: Near the beginning of the movie, when Kevin Costner is going to deliver the dead mother's premature baby, he tells the nurse "Get pre-natal down here." It should be "neo-natal" since it is the neo-natal unit that cares for premature babies. Pre-natal pertains to the care of the mother and baby during pregnancy, neo-natal to the care of prematurely delivered babies.
Continuity mistake: When Kevin Costner first meets the Venezuelan pilot who takes him into the jungle, he pulls his wife's picture from his pocket. You can see in the that split second that the picture is of 3 waterfalls, but when the closeup is shown from the pilot's point of view, the picture is different.