Continuity mistake: The professor mentions he can't drink vodka with the Russians because he's allergic to alcohol, yet in the episode "Man With A Net" (with Lord Beesley), he drinks a strong alchoholic drink he made along with everyone else with no signs of any sickness, or reaction preventing him from drinking it.
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: 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.