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.
Continuity mistake: When Kevin Costner goes to the Catholic school to talk to Linda Hunt, he parks his car very quickly and badly at the curb, with the back end sticking out in the street. When he comes back out after being told the police are on their way, we see him walking down the sidewalk towards his car, which is now parked neatly next to the curb.
Audio problem: When Costner finds his baby, The native lady hands it to him - you can hear the baby cooing happily, but if you look closely at the baby's face you will see that she is crying.
Factual error: A young boy is brought into a paediatric emergency room, where after trying measures to save him fail and he dies - he has no heartbeat. So they use a defibrillator on him, but that's the problem: You can not use the defibrillator on someone with no heart beat, who has flatlined. The heart is an electric pump; with no spark, there is nothing to jump.