Continuity mistake: When they arrive on the island of Talos, the bronze giant, Hercules and Hylus find the statues atop huge plinths. In close up, they are looking up at the statue of Talos, then in a wide shot they start to walk towards it across bare rocks, then in close up they are back where they were with plants behind them.
Continuity mistake: When Talos comes after the Argonauts, he reaches his hand through an archway in the rocks. After he withdraws his hand (in Harryhausen stop motion), notice one of the Argonauts wriggling and struggling against the rocks as if still trying to get away - the actor doesn't know what the end shot will be like and is still hamming long after the hand is gone.
Continuity mistake: After Talos destroys the Argo, Jason swims to the statue of Hera. It is obvious he is in a pool because the water colour has changed, the water is lapping slightly (like a pool and not the ocean) and finally Hera seems to be propped up by something as she isn't moving with the tide.
Continuity mistake: At the start of the final battle with the skeletons, Jason and his companions draw their swords and release the shoulder straps that are holding the scabbards, allowing them to fall. During the close-ups of Jason before the skeletons attack, his scabbard strap is back where it was.
Continuity mistake: When the giant bronze statue, Talos, attacks the Argo, the crew flees across the beach and up the ship's boarding ramp, and one sailor chops through a mooring line so the Argo can escape. But, in subsequent shots as the Argo departs, no chopped-off mooring line remains on the wide-open beach, and there's nothing to which they could tie a mooring line, anyway.