Factual error: At one point in the movie the sun is behind the helicopter and we can see that the places for the missiles are empty. However, he's shooting right after that.
Factual error: The soviet military equipment isn't all that Soviet ... e.g. the helicopter is supposed to be a "Mil-Mi 24 Hind" (Pilot and system operator sitting behind each other), in fact it's just a French "aerospatiale puma" with additional mock turrets and so on (crew sits side by side).
Continuity mistake: Rambo has a cut on his left cheek bone that is forever getting smaller, bigger, scabby and in some scenes it's gone. Sometimes it's white, sometimes red. This all happens in one day.
Revealing mistake: Rambo, Trautman, and the Afghan prisoners are escaping the fortress by stealing the Soviet helicopter, and Rambo is preparing for liftoff. There is a close-in shot of the Soviet helicopter's rotor shaft, on which can be seen a small American flag.
Continuity mistake: When Col. Zaysen says, "We are wiping out no one." to Col. Trautman, you see Zaysen holding a chess brick in front of him. When it cuts he is holding the brick away. (00:23:00)
Factual error: When Rambo is going through the Soviet minefield, he probes a couple of times very hard with his knife, and then he lunges forward. Now, jabbing hard into the ground where you think there might be an explosive device is as bad an idea as it sounds. Also, Rambo doesn't probe to the sides where his elbows and knees are going to support his weight. Also, he lunges forward farther than he had probed. And finally, the mine he does find is very big for an antipersonnel mine. It looks big enough to be an antitank mine.
Suggested correction: Whilst generally speaking, you are correct, Rambo jabs in at an angle for the mines which is a technique still used today by some special forces. Many works of fiction written by real-life special forces members will state this method. If the producers had chosen to show Rambo clearing the minefield properly, the scene would have taken much longer than it does. The mine at the end, may well be an anti-personnel mine however, this does not make it a mistake, it would still do the job required.
Revealing mistake: When the Afghan village is attacked by the two choppers you see a lady running with a baby. It is quite obvious she is carrying a doll instead of a real baby. (00:41:15)
Continuity mistake: Inside the Russian fort, Rambo throws a hand grenade at a wooden door. If you look closely, the door explodes from the other side, NOT the grenade side.
Continuity mistake: In the scene where Rambo is stick fighting and the other guy is on the ground and submits. Rambo reaches down with the stick to help him up with his right hand. Then in the next shot it shows Rambo pulling him up with the stick with his left hand. (00:05:40)
Revealing mistake: The character Zayasen is played the French actor Marc de Jonge, who does really well despite that French words are at times substituted for Russian (e.g. "maintenant" is the French for "now", "chercher" means "to search". When he says (in Russian ),"Keep searching ['cherchez'] for the Americans. I have to return and refuel now ['maintenant']",and "I want every trooper on the border now ['maintenant']".
Continuity mistake: In the beginning when the man shows the picture of Rambo to the man behind the desk, he flips the picture twice during the shots. (00:01:10)
Continuity mistake: Inside the castle, at the Russian base, Rambo picks up a rifle of the AK-family with a front grip, but it is not an Ak-47. Then, in the middle of firing, when the camera angle changes, his rifle has turned into an Ak-47.
Continuity mistake: Rambo plays a game where you have to pick up a dead sheep and throw it into a circle. He reaches down from his horse to pick up a huge, black, fake and dry sheep with his right arm. The next scene shows him with a small, wet, real dead sheep but now it's in his left hand. (00:39:35)
Continuity mistake: A soldier in Pakistan runs and grabs his arm which has blood on it from a bomb that goes off a split second later. Bad timing.
Continuity mistake: When Rambo goes through the mine field his knife changes. Sometimes it has saw teeth(like the one in First Blood) and sometimes not. You'll see it when he finds the mine. Stallone wasn't satisfied with master knife maker Gil Hibben's first model for the movie and the knife was changed after the mine field scene was shot and some close ups of the new Rambo knife were made later on. (00:47:15)