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: 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 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: 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: Gilligan fails 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: 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.