Plot hole: In order to build up suspense, Virgil and Brains stand on the Crab Logger as its dangerous fuel is pumped out, despite the fact that it is hanging on the edge of a precipice. In fact they could have left as soon as they had plumbed in the pipes to empty the fuel tanks - the whole procedure is controlled by Scott in Thunderbird 1 and they make absolutely no contribution to the operation at all. They do not need to disconnect the pipes; they are left behind and dropped from Thunderbird 1 as planned. They just stand there chatting about how much danger they are in until jumping clear at the very last second. Silly buggers.
Plot hole: The scientist yells for Igor to capture the escaping Castaways, to which Igor responds "capture them yourself" in Ginger's voice. The scientist appears surprised to find out Igor is not Igor, but how can this be? He had to be the one to pull the lever to switch everyone's personalities and bodies around, so he should have already known.
Plot hole: Solo blows open the ceiling vent of Illya and Marion's cell, and she stands on Illya's shoulders until Solo can reach her and pull her out. This leaves Illya with nothing/no one to stand on, no way to reach the vent and no apparent way out of the cell. But he's out just the same in the next scene, with no explanation as to how. (00:42:40)
Continuity mistake: When Drake is leaning against the back of the park bench while talking to the tailor, in the shots over his shoulder, his watch is partially covered by his shirt cuff. In the shots from in front, his watch is completely exposed, despite his arm never moving. (00:12:25 - 00:13:00)
Factual error: The sea plane that lands to rescue Savage at the end is a type not built until after the war. And it's marked "U.S. Air Force," an entity that also didn't exist until after the war. During WWII, what later became the Air Force was known as the U.S. Army Air Corps.
Continuity mistake: Simpson is trying to pull a baby elephant onto his boat when the rope snaps, causing him to fall into the water port side. You can see the end of the broken rope going with him. Next camera angle, the rope is wrapped around the cleat and Simpson is being towed behind the stern. (00:18:55)