Lobsters are not found in the South Pacific.
When the walls of the hut collapse during the sleep test it's obvious that Gilligan and Skipper aren't actually inside.
The Characters state that they are on the highest point of the Island, yet there are mountains behind them.
The Professor, relying solely on a measuring stick (while ignoring the unchanging shoreline) to conclude that the island is sinking, displays astoundingly poor deductive skills and a questionable knowledge of geology.