When trying to demonstrate his invention to Gilligan in the dream sequence, the Professor claims his wheel doesn't work. Later on, however, towards the end of the dream sequence, the castaways are using the same wheel to transport supplies.
The professor contradicts himself first calling the tablets Egyptian and then later Cuneiform (Sumerian).
The Professor's "mistake" really isn't a mistake at all. If you're reading a map and want to reverse your starting and ending points, you just look at it the other way around. Once they realized the map showed how to get *to* the island, reversing it would show how to get *away* from the island.
Writing had not been invented a million years ago.
Neither Egyptian nor Sumerian writing could have been found on a Island in the Pacific.
While trying to decipher the native's map, the Professor says that he can read Egyptian hieroglyphics. The native's drawing is completely unrelated to hieroglyphics and knowledge of it would be of no use whatever.