After Allen and Kornbluth scuffle in the dentist's office and Kornbluth sits in the chair, the paper bib around his neck has been torn off. The bib is back in the next shot, then gone again as they leave the office.
When Fat Jack's boat starts spinning around Allen, a cover appears over the motor that wasn't there before. In the next shot, it's missing again.
When Madison meets Allen on the beach, after rescuing him, her hair changes from wavy to straight several times before she re-enters the water.
When Allen and Dr. Kornbluth rescue Madison from the lab, her tank is full of nasty-looking, cloudy water. However, when the scientists enter the lab and find Alan's brother sitting over the tank "fishing", the water is crystal clear.
The moon is waning when it should be waxing.
Madison says she has only six days and must return when the moon is full. Twice when the moon is shown, the phase is of about a week after full moon rather than a week before full moon. The dark sliver should be on the left rather than the right.
Tom Hanks' character is listed as Allen Bauer in the ending credits, as well as on his drivers license in the wallet that Madison finds on the ocean floor. However, at the beginning of the film, the name plate on the door of the office which he and Freddie share shows his first name spelled as Alan.
Joe Cirillo is credited as playing "Sergeant Munson", but his name badge in the movie reads "Edwards".
Allen hails a cab without his tuxedo jacket on or in his hands, yet he has it by the time he arrives at Cape Cod. If you look closely, you can see the jacket tied around his waist; a buttonhole rests against his hip.
When Madison is in front of the televisions at Bloomingdale's, Allen asks what her name is. She replies in loud, screeching tones, shattering the televisions. When one television's screen breaks, it is clearly caused by a remote-controlled explosive, and the screen is clearly made of cardboard, not glass. It also shows the circuitry behind the picture tube, not the tube itself.
In the final car chase sequence, 2 men play chess in front of a clear walkway. When Allen and Madison pass them, a flock of pigeons suddenly appears and rises into the air. When Allen drives in reverse to escape, the same pigeons fly backwards.
While diving, the scuba tank on Kornbluth's back is clearly fake. If it was a backup air source, the pinched-off air hose from the boat wouldn't have mattered.
When Madison runs back into the water after kissing Allen on the beach, she has tan lines on her back, even though she had never been out of the water before, suggesting that Daryl Hannah had been wearing a bra before shooting that scene.
When Madison is exposed as a mermaid and dragged into a car, her legs and knees are visible as shapes in the fishtail.
When Madison reminds Allen of their first encounter, she states that Allen fell off the ship. In 1964, Allen jumped over the railing of the ship rather than fell off of it. He fell off a boat in 1984 when Madison rescued him.
When Madison enters Bloomingdale's, Ron Howard is reflected in one of the mirrors.
In the final sequence, bubbles from safety diver are visible ahead of Madison and Allen.
During the final car chase, Allen's BMW weaves around a taxi cab that has stopped in the intersection coming from the side. At the left of the screen you can see that the car also just misses a camera. This is the camera that captures the military truck going around the same cab in the next shot.
During the final sequence in which Madison rescues Allen from the divers, she uses her tail twice to defend herself. In both instances, a hand is seen positioning a tail prop against the divers.
After Allen and Madison jump into the water at the end of the movie and fend off the frogmen, they immediately come upon a coral reef and other aquatic features that appear tropical and which would not be found in the Hudson River/New York Harbor.
When Allen falls into the water after Fat Jack's boat hits him, his wallet falls out of his pocket and rests on a coral reef. The ocean off Cape Cod is much too cold for coral reefs.
Madison learns to speak English by spending the day in Bloomingdale's, watching TV. But before this, in Cape Cod, after finding Allen's wallet, she is able to determine where Allen lives by reading the wallet and the map in the sunken ship. Even after Madison learns to speak English, there's no indication that she's learned to read it.
Allen's wallet, credit cards, and money were in Cape Cod. It is never explained how he got back to New York.
It is never mentioned as to what was so valuable about Madison's necklace that she was able to trade it to have a large water fountain installed in Allen's apartment.
When Eugene Levy/Tom Hanks escape with Madison from the lab, they run out the front hysterically screaming at the back guard.. the next scene they are on the front steps going to the car, clearly having left the way they came in. Then the real 'Swedes' show up at the front guard, and he is sitting calmly at his desk.
When Madison takes a saltwater bath, the water is steaming. Madison wouldn't live in hot water, so it seems very odd that she does not want to take a cold water bath.
When Madison is forced to change back in public, you can see her tail is through one leg hole of the panties she was wearing. This doesn't make sense in the fabric between the hole should have been torn apart when her legs turned back.
Before Allen and Madison leave for the dinner with the President, Allen presses the up button on the outside of the elevator. They are on the fourth floor, so Allen should have pressed the down button.