Continuity mistake: We see a shot of the outside of Ginger's hut when she and the Skipper are first planning for the beauty contest. The door to the hut has a window in it and we can see the Skipper's hand leaning on the sill. We cut inside and suddenly Ginger is by the door and the window has vanished.
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?
Other mistake: After Gilligan gets up to take the sand to Mary Ann, the camera closes in on the box lid. After it does, the picture goes into a freeze frame because the ripples in the water of the lagoon stop dead still for the few seconds until the dissolve into the next scene.Movie Nut
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.