As the Howells are asking Gilligan questions to find out about why the Skipper seemed so upset (because of the upcoming tidal wave), Mr Howell is standing with his hands in front of himself as he's speaking. In the next camera shot, his hands are on his hips.
When the castaways head out on their reunion cruise, the S.S. Minnow II is shown from a distance, with the Skipper shown driving the boat with Gilligan on his left. When the camera shot changes to a close-up, Gilligan is on his right.
After saving Mr Howell when he fell into the ocean, the Professor gets back in the floating hut with his hair wet & matted down. A few minutes later, he sticks his head out of the back of the hut to look for Gilligan and his hair is completely dry and groomed.
In the first shot when the huts were shown being towed into the harbor, there was clearly some kind of boat along side of it, but then that boat disappears for the rest of the scene.
When Gilligan is being pulled in the ocean by the shark, the castaways run to the other side of the hut to watch, with the Professor to the left of Mrs Howell. In various camera shots, he is shown to the right of Mrs Howell.
All of the products that the Professor tried to invent after being rescued were available on the market before the castaways were first marooned, so he should have known about them. Frisbee was introduced 1950, electric toothbrush in 1960, pantyhose and skateboards in 1959. In fact, Gilligan mentioned wanting a skateboard in an episode of the original show.
While it was obviously done for dramatic purposes and for show, the castaways would never have been pulled home in their huts. The Coast Guard would have brought them aboard a cutter and made them abandon the huts.
While the castaways are standing on the dock being interviewed by the Governor of Hawaii's assistant right after their rescue, the assistant mentions two American Presidents, Jimmy Carter and Gerald Ford, and Watergate. The castaways seem not to know who these people or events were, but they did have a working radio on the island, so they should have been entirely familiar with each one of them. However, as mentioned in the beginning by the Professor, the radio had died some years back, so they could've really been out of touch with current affairs all this time.
When the castaways are on their Hut Boat and they decide to make a Sail out of their clothes. They show all of their clothes in the sail and then in the next scene they all have their clothes on that they made the sail out of. The sail was made from the Howell's excess clothing (which can be argued was nowhere to be found in the huts) as Mr. Howell clearly offered up to make the sail. (This could've been done as to prevent the castaways from stripping down to their undergarments, which likely would not have passed network censors at the time.)
In the time Gilligan went to get the mail and returned, somehow "Minnow II" was painted in entirety on the back of the boat, when it wasn't there at all before. Even after speaking with the spies at first, not enough time had gone by to finish such a perfect paint job of the boat's name.
At the beginning of the movie, Mr Howell is wearing glasses. He never had glasses before.
During Gilligan's tow with the sharks, visible on the water are reflections of land and the occasional glimpse of land at the top of the frame.
When Gilligan is being pulled by the shark, while they're in the middle of the ocean, you can clearly see parts of the shoreline and reflections from trees in the water.
After the storm and they adrift out in the sea, Mr. Howell falls in the water and the professor jumps in after him, it is obvious Mr. Howell is standing in four feet of water.
When the castaways finally paddle ashore, Skipper, Gilligan, and both Howells are still wearing their hats.
The Skipper and Gilligan are supposed to be in Hawaii, but every boat shown in the marina has a boat registry number that starts with CF, which is for a water craft of any kind registered in California.
At the beginning of the movie when Gilligan is talking to the Skipper, you can clearly hear quail calls in the background. Quail do not live in tropical climates.
Normally people missing for 7 years are declared legally dead. People missing for 15 years certainly would have been declared dead, and their assets distributed through the probate process. Having this reversed and legal identities restored can be a very long and complicated process. One can assume this would particularly affect the Howells, yet there is no mention of any of this in the film.
It is puzzling why the castaways would have a reunion so soon after their rescue and on a boat. Most reunions take place years after everyone has parted ways and giving their previous experience, would not have the reunion on a boat.
At the end of the movie, the castaways don't realize where they are, but how could they not?? They paddled into the lagoon, something they had seen every single day for 15 years.
In one of the episodes, where Mary Ann fakes having a boyfriend & mentions him by name, in that episode, the boyfriend she fakes ends up full bodied & played by an actor when The Skipper & Gilligan show up to Mary Ann's pending nups to the boyfriend she faked back on the island.