In the opening credits, the S.S. Minnow that is shown before the cruise, and after beaching on the island is different of the one shown during the storm. (No upper deck above the windows where the helm is, and the front of the cabin is straight, rather than pointed.)
In Gilligan's Island: Two on a Raft, just as the Skipper and Gilligan finish fighting off the sharks, the Skipper's hat falls off his head and into the water right in the path of one of the sharks, and it looks as though the shark was going to make off with it, but in the next shot the hat is back on the Skipper's head, or perhaps he had a spare hat, like a spare tire.
In Gilligan's Island: Love Me, Love My Skipper, when Gilligan comes swinging into the party as Tarzan, the first shot has him in control as he starts his swing, but the second shot of him has him out of control and on the upswing as he crashes into whatever was on the table, then in the third shot of him he's in control and on the downswing when he swings between the Skipper and Professor and into the hut's wall.
In Gilligan's Island: Allergy Time when Gilligan is packing and the Skipper is snuffing the candle with his sneezing, the crew member who blows out the candle is visible on the right of the screen during the sneeze when Gilligan holds up the board in front of the Skipper.
Episode, Gilligan's Island: X Marks the Spot, the radio announcer gives the target coordinates for the Powderkeg missile as 140 degrees latitude, 10 degrees longitude, which the Skipper (an old salt in these waters) and Professor confirm. Lines of latitude only go up to 90 degrees. Transposing the coordinates, though (to 10 degrees N latitude, 140 degrees W longitude) would place the missile several hundred miles southeast of Hawaii - the approximate location of their island.
Occasionally the radio announcer would announce the call sign of the radio station the castaways were listening to, and it would always start with W. With few exceptions (and even those don't go any further west than Texas), radio stations with call signs that start with W are east of the Mississippi River. The castaways were somewhere in the South Pacific and had only an AM radio, and even on a clear night, the strongest AM radio station east of the Mississippi couldn't have reached them.
On the episode with the Russian Cosmonauts, Gilligan's Island: Nyet, Nyet, Not Yet when they are drinking and Ivan is passed out on the table, the bottle in his hand is the one marked with the X which was to be the one with water in it. And then Igor asks to drink from the other bottle (because "theirs is empty"), which would then be the Vodka bottle that Gilligan is holding. But you can clearly see the X on the bottle that Ivan is holding while lying on the table.