In the final chase scene between Rambo's Huey and the Soviet Hind helicopter, you can see daylight passing through the missile pods on the Soviet Hind, indicating that they are empty, but the helicopter fires them several times.
When Rambo is preparing his weapons on the helicopter, he has a case of four explosive arrowheads. Throughout the movie he fires five.
Although he does it seemingly instantly in the movie, it would have taken Rambo a long time to cover himself from head to toe with thick mud, then clean it all off immediately after he killed the soldier.
Rambo's helicopter makes a crash landing in the water. Colonel Podovsky closes in with his helicopter and is about to fire a missile. A closeup of Rambo's helicopter shows a hole in the windshield, but when it cuts to the wide camera shot, there is no hole in the windshield. It cuts back to the closeup, and there is a hole in the windshield, which Rambo fires a rocket launcher through.
When Rambo is trashing the control hut at the end of the movie, the length of the ammunition belt gets progressively smaller but then increases again before finally running out.
Backfire from a rocket launcher would fry the entire crew of the helicopter.
Just before Rambo parachutes into Vietnam, they say that he will be dropped from a ceiling of just 250 feet. This is much to low for any parachute to fully deploy and safely land the jumper from a moving aircraft.
When Rambo is jumping into Vietnam, he becomes a "towed jumper" by a piece of equipment that gets snagged on the doorway. Before the Airborne operation took place, a Jumpmaster (the guy inside the plane observing the jump) would have ensured there was no such obstructions on the doorway for that exact reason. Also, protocol for a towed jumper is to immediately cut the snagged piece of equipment free, releasing the jumper as close to the drop zone as possible.
During Rambo's insertion, he is aboard a converted executive jet with "low" wings and side-mounted jet engines. He jumps out of the side door in front of an engine. Actual parachute jumps are performed from aircraft with top-mounted wings from behind the engines to prevent jumper getting caught up in the wings and engines.
The exploding mortar shell which goes off behind Rambo and the POW during the rice paddy ambush - both men would be killed in reality since the mortar shell has enough shrapnel to inflict third degree burns and blunt trauma.
Rambo fires the explosive arrowheads at two trucks on the bridge, yet in the next shot the center truck is seen burning as well. However, the center truck could have caught fire from the other two explosions.
When the Soviets are electrocuting Rambo, the lights around the compound flicker. Rambo throws the Soviet guy onto the fence and then turns the electricity on full blast, and leaves it on. The lights around the compound do not flicker at all.
Smoke machine visible in the passenger compartment as Rambo lands the damaged helicopter.
When Vietnamese soldiers are shooting at Rambo from the bridge, they clearly run directly in front of each other's guns while firing.
When a Vietnamese soldier is caught in the cane fire, and falls to the ground in flames, his fireproof gloves are visible.
When Yushin drops the incendiary bomb on Rambo at the waterfall, rather than one detonation there are many on the various outcroppings.
At the end of the movie where Rambo is walking out of the HQ to where he landed his downed chopper, there are various crews with equipment for fire-control (fire extinguishers/fire hoses) but do not use any to put out the flames. You can see them jumping around the flames but the fire is not contained or put out.
The US made PBR (Patrol Boat, Riverine) that Rambo destroys with the RPG is flying the blue & red flag of the Viet Cong. However, the Viet Cong was formally disbanded in 1976. By the time of the film only the red flag of the Socialist Republic of Vietnam would be used by all military units.
During the escape from the POW camp, Co is using a suppressed sub-machine gun (a 9mm Ingram MAC-10): however, its shots are dubbed exactly the same as Rambo's AK-47 (a 7.62mm assault rifle).
The big Russian guy orders the gunner to shoot in the water, and when Rambo shouts while being tortured, his mouth is closed.
Rambo uses the chicken and gas trick to set the village on fire, then uses his exploding arrows to set off more explosions. One Vietnamese soldier stumbles out of the tall grass on fire. When he falls to the ground, you can see him wearing a heavy glove to protect him from the fire.
After Rambo buries Co, the shot switches to a dolly of several Soviet soldiers walking through the jungle. Through a break in the leaves, two crew members are visible walking in the river, one in a bright blue tank top and the second in black clothing.
About an hour into the movie, Rambo is struggling with the 'big' Soviet guy in the back of the helicopter. After he manages to throw him out, he then takes control of the Soviets' helicopter. Once he is seated in the pilot's seat, you get a front cameo shot of his face and in the background, you see another helicopter right on his tail (Rambo even turns around and takes a glance at the helicopter on his lead). Yet in the next panoramic shot of Rambo's helicopter skimming over the jungles of Vietnam, you see no helicopter.
When Rambo fires the first rocket at the Vietnam People's Army (VPA) camp after
seizing the chopper, a man in a flight suit can briefly be seen in the cabin of the chopper.
While many Soviet soldiers scour the woods searching for Rambo, he is inexplicably running all around them and killing them off one by one and not one soldier sees him running to and from. Several soldiers would have certainly seen him running around in the woods killing off their fellow comrades.
After his capture Rambo suddenly has his weapons available again.
Colonel Trautman's fatigues are missing his rank insignia (a Colonel's eagle) and his officer branch insignia, which would normally be worn on the lapels. Since his uniform has other insignia, name tapes, and badges, it can't be excused as a "sanitized" special operations uniform.
While Co is walking through the jungle with Rambo, she continually has her finger on the trigger of her AK-47 (or AKM). This violates a basic firearm safety rule, known to every soldier and guerrilla, which states that the finger must stay off the trigger until the sights are on the target.
When he sees that Rambo is going to radio to his base, Lt Col Podovsky says "very good" in Russian. The way he pronounces it (ochen' khorosho) makes it clear that he doesn't know a single word in Russian.
Rambo would not have needed to cut some of his equipment loose to be free to jump from the plane; he could have just cut the snagged strap.