After Bruce falls out of the runaway speedboat and climbs aboard a fishing boat, he is instantly dry,
At about 14 minutes into the movie, Zach has fallen through the hole left by the missing grate into the debris, before going into the "clean room." Covered with dirt, etc., he goes to talk with Bruce Templeton. Bruce brushes Zach off a little and then seats himself in his office chair and leans back a bit. Bruce's suit jacket has dirt and larger pieces of debris on it. A second or so later when he leans forward, his suit jacket appears completely clean.
When Jenny hits Bruce with the cake near the end, two of the items in the closet switch places.
When Jenny is outside the plant using a payphone to call her dog, she is wearing a different outfit than the one she wears in the preceding and the proceeding scenes.
When Jenny gets her heel stuck in the grate outside the clean room, in the first shot, her left foot is stuck. In the next shot, it's her right foot. When she gets off the grate and leaves her shoe, it's changed position.
Edgar Hill is introduced as a CIA agent investigating reports of spies in the Catalina area. In the 1960s, the CIA did not engage in overt counter Intel ops in America. That would have been the FBI's job.
When Bruce and Jennifer are stargazing, Bruce points out the planet Venus next to the nearly full moon. Venus is closer to the Sun than Earth. Therefore, it would only appear near the moon when the moon is in the waxing or waning crescent phase.
When Bruce is showing Jennifer around the kitchen, he peels and eats a banana and drops the peel on the floor for the robotic vacuum to pick up. Later, while talking to the CIA, he says "I hate bananas!" However, he pretended to like bananas solely to impress Jennifer; therefore, he is not making a mistake but, instead being consistent.
Wires are visible in both scenes set in the NASA anti-gravity chamber; first on the test astronaut, and also when Jennifer accidentally enters the room.
In the two scenes where the runaway boat crashes onto the beach, the cars around the boat seem to rearrange themselves from shot to shot. A closer look at which car ends up where, reveals, apparently, the wide shot intended for the first scene was mistakenly edited into the second one and vice versa.
When the Venus Project is underway, and Bruce and Jennifer are working late in a remote location, they watch a test launch from behind a protective shield. A close-up of the launch ignition is shown, then moments later when Jennifer is behind the shield, the same launch ignition is shown as a reflection, but not reversed as the mirror image it should be.
When Bruce snags Jennifer's mermaid tail with his fishing line and reels it in without her, she surfaces and says she's bottomless, but as she swims away, her pink/flesh-colored bikini bottoms are visible.
In the beginning of the film, a hook can be seen holding Jennifer in position underwater.
When they are singing the theme song at dinner with Jennifer's family, at about one minute into her rendition she apparently made a mistake in beginning the wrong verse--a fleeting expression of panic crosses her face and she holds her hand up to her mouth, and then smiles and reaches toward the Captain. All the actors stayed in character and continued with the performance, so the creators evidently decided to leave in that shot despite Doris Day's reaction to her mistake.
When Bruce Templeton (Rod Taylor) is escorting Jenny across the plant in a golf-cart type vehicle, someone calls out a greeting to "Mr. Taylor" rather than to "Mr. Templeton."
When riding in the remote-controlled speedboat the first time, Bruce explains that the device for controlling the boat is called RIMCOP. He explains that this stands for Robot Inshore Manned Observation Post. This would then be RIMOP not RIMCOP.