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: This movie was made so the castaways could be rescued, but how could they be found? The map the Skipper was pointing to didn't have anything on it that could realistically show where they exactly were, and all scenes in the film wouldn't help them get found at all, just made for good laughs.
Plot hole: This was obviously bad script writing, but let's figure out carefully how this failed rescue attempt (by Gilligan) doesn't really make sense. The two Russians were to be picked up at 11:00. When the castaways appear at the Russians' location, the Russians are gone. Gilligan states it's 8:00 according to his watch, due to the unaware fact he set his watch to Manila time (3 hours earlier). He claims to have set his watch when it was 10:30 in Manila - Skipper then yells there's 3 hrs difference between the island and Manila, so Gilligan sets his watch ahead 3 hrs and it's now 11:00. Here's the mistake: if it was 10:30 in Manila and there's a 3 hr. difference, it would have been 1:30 on the island, and also if Gilligan's watch stated it's 8:00 now (Manila time), he would have set it to 7:30 when hearing the 10:30 announcement on Manila radio (which he didn't do). Lots of these times just don't make sense.
Plot hole: Gilligan admits he put the Professor's measuring stick in deeper and deeper waters to catch bigger lobster. So wouldn't the Professor have noticed the stick has been moved further out (and more than once too) in the water rather than think the island is sinking? He always had all positions and locations down to a science in many episodes, so how could this have gotten past him?
Plot hole: During all their filming for their "silent" movie, the castaways are using talking in actual dialog to explain their overall situations on the island, but when played back at the end, it's just showing them all talking sped up without hearing voices being a silent picture. What was the point of them filming then with actual words? They may as well just moved their mouths randomly without actual words coming out. In addition, where did the "music" come from throughout the movie?
Plot hole: Gilligan foils the rescue attempt by saying that before the storm, he wrapped up the telephone wires real good with the professor's rubber glue so they won't get wet... But the scene before this, all castaways were testing the phone when a storm instantly hit them without warning. Gilligan wouldn't have wrapped up the wires since there was no storm til the last second (in which they all ran and abandoned the wires).
Plot hole: Most of the episode focuses on just Gilligan and the Skipper riding the capsule out to sea (although the Howells and the girls attempt to stow away with them at first). However the whole plot changes at the end... suddenly with nobody aboard the capsule, Gilligan tells the Skipper it floated off and Skipper yells at him saying "We could have ALL been on that capsule!" when it suddenly explodes thus saving everybody as if the plot now called for everyone to have been on board. It was still supposed to be Gilligan and Skipper only.
Plot hole: Many episodes show either visitors on the island swimming away or objects floating away on rafts (a lion, a silent film, etc) that at the end of the episode always make it safely to civilization (as heard on the radio)... yet, none of the castaways ever could swim or leave on a raft to attempt to get off the island and get rescued in the same way.
Plot hole: On many different occasions, the castaways meet a wide variety of people who say that they have been on the island for either ten or more years thinking they were the only ones on the island before the SS Minnow even arrived. With so many people who had been on the island for such an extended time, it seems kind of strange that none of them had ever met one another.
Plot hole: Mr. Howell suggests the switching vodka for water idea, and then Gilligan empties one vodka bottle and puts water in it for the castaways. But there's no way this plan could have gone through since no castaway knew in advance how much vodka or how many bottles the Russians had to execute such a plan.