As Ginger leaves the cave after the entrance is sealed with a rockslide, she bemoans that her dress is damaged, as it's her only one. But throughout the series, she's shown wearing many other outfits.
As the radio announcer runs down the list of the passengers, the Professor is standing, hands on hips, as his portion is read. But in the immediate next shot, he's sitting on the sand, legs outstretched in front, in [what becomes] the well-known closing scene of the series.
When Gilligan's disguises himself in a tree trunk, a woodpecker starts pecking his head. But woodpeckers are not endemic to oceanic islands.
As the castaways run in and out of the cave near the end of the show, it can be seen that there is a bright light inside the cave shining on them.
It's impossible for Ginger to take her entire wardrobe on a short ocean tour (as can be seen throughout the series).
Considering the vastness of the Pacific Ocean, the chances of the Skipper and Gilligan landing on the same island twice are likely a billion to one.
When Gilligan first gets his oar bitten and the Skipper says keep paddling. You can see the shadow of the boom mic on the raft in the lower left of the screen.
When Gilligan is first showing the Skipper the raft the shadow of the boom mic is visible on the first log in the lower right of the video.
In the opening theme Mr. Howell is described as a millionaire but in the radio announcement at 2:40 the announcer describes Mr. Howell as a billionaire.