Revealing mistake: At the Tower of the Serpent, after Conan and Subotai steal the Eye of the Serpent and also kill Doom's giant pet snake, Conan and Subotai make their escape; and when Valeria grabs the rope for her own escape, we can see the stunt cable used to lift her (I'm providing my own screenshots for my mistake). (00:48:05)
Other mistake: When Conan gathers flowers to "take to the girl", the flowers that he is holding as he mounts his camel, are very long-stemmed, and dark purple in color. In the next scene he is riding the camel and the flowers he is holding are not only very changing color as another post indicated, but they are also very fake plastic / fabric flowers. In the same scene, Conan is then seen wearing a strong of flowers around his neck, those too are very fake flowers. (01:05:00)
Continuity mistake: While the dogs are chasing Conan, the sun changes between shots.
Continuity mistake: When Conan is about to climb into the tunnel that leads to the snake pit, he has a dagger and on his back his sword, but when he is inside the snake pit, the sword is gone.
Audio problem: When the wizard arrives with weapons and armour, he is about to trip and mumbles out loud, but his mouth doesn't move. Neither does Subotai's when he asks him, "Hey, old man, where did you get this stuff?" (01:45:25)
Revealing mistake: When Valeria cuts a soldier's throat, a protective pad over his belly protrudes under his shirt.
Continuity mistake: When Valeria fights a guard, his helmet falls off. A second later, she beheads him, and his helmet is back on.
Continuity mistake: When Conan is captured and Thulsa scolds him for killing his snake, Conan's cloth is in rags by his elbow. Then in a close-up the cloth is not that torn apart and it's over his shoulder. Then a baddie rips it and back to a wide angle with the cloth in rags by Conan's elbow again. The close-up angle should've come first of all.
Continuity mistake: When Conan cuts off Thulsa Doom's head, Thulsa's arm swaps between bent or extended depending on the shots.
Continuity mistake: When Conan pushes the huge cauldron there's a man by the stairs who disappears in the immediate following angle.
Revealing mistake: After Conan pushes the heavy cauldron to spill the green liquid, the cauldron falls off and bounces like a football, revealing it's a prop.
Revealing mistake: When Conan kills the baddies in the orgy, he aims a blow at a man's neck, then punches a guy standing next to a column (and later stabs his stomach), but his punch misses by far.
Continuity mistake: When Valeria tries to grab the jewels Conan his fist is under his chin. A shot later it's on his cheek.
Continuity mistake: When Conan enters the witch's place and she throws something in the fireplace, he has his hand by his mouth. When the angle changes it's further away, next to his right shoulder.
Continuity mistake: When Conan is inside the cave and finds the sword, he turns his left hand around to grab the handle, but a shot later from a different angle his hand is in a totally different position, holding the sword from someplace else.
Revealing mistake: When the movie begins and Conan's father is talking, watch the pattern of the blue-screened clouds behind. The same clip is being repeated over and over again.
Continuity mistake: After Conan ends fighting in the ring he takes his hand to his neck, hair covering it. A shot later his hand is over his hair.
Revealing mistake: When the dogs are eating Conan's dad, he is replaced by an obvious stuntman with a noticeable wig.
Continuity mistake: After Conan's dad dies two baddies walk towards the kid. The second one sheathes his sword twice.
Revealing mistake: When Conan is fighting in the ring and smashes a guy's body against some [prop] rocks, the painting cracks and falls off.
Answer: Not in the movies, but in the original books. He escaped by grinding his chain between two millstones until it broke.
Twotall