When Ben spills milk on his mother's plans, he picks up the carton. In the next shot the carton is on its side again.
The wheel of the ship changes from metal to wood and back again.
When the Harvey family is trying to get back on the boat from San Juan, Benjamin is seen with a tattoo on his chest, he then shows his mother that it wipes off by removing half of it. In a later scene, the full tattoo is back
The lifeboat for The Wanderer appears and disappears throughout the entire movie. In the first scenes it is on the cabin roof to the left of the steering wheel where, in fact it is sitting in the cradle that was designed to hold the life boat, soon after it's on the deck sideways, then the boat is nowhere to be seen at all, then it is back again and so on for the entire movie.
In Cuba, Captain Ron drives to the dock and hits the pirate's truck. The left headlight is lit immediately after impact and is broken/burnt out when he backs up to rescue the family.
While being chased in Cuba, they are being chased by an early 60s Ford truck, and there is a 70s Dodge truck in the background. No American cars have been imported into Cuba since 1959.
Numerous times during the movie, the boat is supposed to be under sail. However, the boom is visible swinging freely back and forth above the helm. This would not happen unless the boat was heading directly into the wind (in which case they would not be moving) because the wind would push the sail to one side
When they are arrested at the Carnival in San Juan they are met at the jail by an official of the US Department of State. San Juan is in Puerto Rico, a US Commonwealth - the US State Department has no role in what would be a matter for local law enforcement. Furthermore, US citizens can no more be deported than someone could be thrown out of the State of California or Pennsylvania.
In the scene where calypso band plays on the dock, as Captain Ron first pilots the Wanderer into the harbor, the Fender bass is not plugged into an amplifier. It would be impossible to hear the bass, unless it is plugged in.
When Caroline runs into the house to announce her engagement, it appears she overruns her mark, as she looks to her left at the floor as she runs in, then quickly moves back to the mark before speaking to her parents.
When Captain Ron explains to Benjamin Salisbury (Ben) what his parents were doing below decks, Ben spits out his beer into his hand. However, Ben starts to lift his hand too early indicating he is going to spit out the beer before Captain Ron gets to the punch line.
When the Harveys are seen at the beginning they have barely left the dock, yet in a few shots later they are seen far off the dock.
When they are pulling into St. Haag when captain Ron takes over for Martin at the helm he down gears down the boat. It then shows the boat from the water and the camera panning back up with nobody at the helm. Then it cuts away and with them both back at helm with Martin telling captain Ron to slow down.
When Martin is in the elevator at the beginning of the movie he is disgusted as a lady sneezes in his cup of coffee which he bought in the lobby. When he gets out of the elevator, it is clear that the cup is not only empty, but unused.
When Caroline is with her "fiance" and she gets out of the truck and runs across the road to the house, it's clearly not Meadow Sisto (Caroline)
When the pirates are shooting at the boat, we hear Captian Ron say, "Aw, geez, gunfire!" but his lips never move.
When the man with the gun is yelling at Captain Ron his lips are not moving although he is shouting.
In Miami, Martin says (in voice over) that Captain Ron hadn't been in the US for more than seven years (something about a statute of limitations) but in another scene Ron said he'd been to Dollywood. At the time this movie came out (1992), Dollywood had only existed for six years. Prior to 1986, the park was named "Silver Dollar City".
During the first game of Monopoly, Captain Ron and Ben settle on 10 cents equals $100. When Captain Ron lands on B&O Railroad, Ben tells him he owes $1.25. It should be 13 cents.