The title song, "The Glass Bottom Boat," is sung during a scene when Jennifer Nelson (Doris Day) invites Bruce Templeton (Rod Taylor) to dinner with her parents. Her father, played by Arthur Godfrey, accompanies Day on his signature instrument, the ukulele, as she sings the song. 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 Godfrey. Godfrey and the other actors stayed in character and continued with the performance, so the creators evidently decided to leave in that shot despite her reaction to her mistake.
When riding in the remote controlled speed boat the first time, Rod Taylor 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.
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.
At about 14 min. into the movie: Zach (Dick Martin) 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 (Rod Taylor). 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 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 we see Jennifer behind the shield, the same launch ignition is shown as a reflection, but not reversed as the mirror image it should be.
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 it 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.
The first time the remote control boat runs up onshore, the cans and boots trailing the boat after the marriage of Jennifer and Bruce can be seen in a quick shot of the boat. It appears they used the same shot for both.
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 you can see her pink/flesh-colored bikini bottoms.
In the two scenes where the runaway boat crashes into 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.