While on the submarine, Zissou inserts a tape into the player. The clock reads 2:18. The camera immediately cuts to Zissou turning the volume up, but the time now reads 1:45.
When Hennessy is speaking to Steve on his boat, there is a stain on his yellow couch that disappears and reappears in between shots.
When Ned is shining his shoes in his cabin and Steve comes to speak with him, the clock goes backwards between shots from 9:50 to 9:40.
When Steve pulls his gun on Jane during the interview, there is an audible thud as if he'd pulled the gun and then lowered it to touch the table, however when the shot changes to face him, he is holding the gun well above the table's surface.
When the team is in the submarine towards the end of the movie Steve's hands are on the steering wheel. As the neon fish swim towards the sub (from the crew perspective) you can see the steering wheel without any hands on it, but when the jump to Steve, he hands remain on the wheel.
When the crew is examining the sunken aircraft, we see the black box which is labeled "Black Box". In reality, airline "black box" flight recorders are colored bright orange.
Steve Zissou demonstrates diving helmets with integrated radio receivers and headphones in order to listen to music under water. As a marine scientist, he would know that radio waves do not propagate in sea water (except very low and extremely low frequencies, both of which need huge antennas to send messages). Given the nature of this film, these diving helmets are due to artistic license.
Ned Plimpton refers to Marcel Prousts novel as consisting of six volumes. Actually, it consists of seven volumes. Six volumes can seen lying on the chair, the first volume is in the hands of Jane Winslett-Richardson.
The word "terrified" is misspelled as "terrifed" in the subtitles early in the movie.
The "Belafonte" model is shown with an observation dome built onto the bow of the ship. It is also mentioned by Zissou. When the ships bow is exposed cresting a wave, there is no evidence of any structure below the waterline at the bow.
After the pirates leave and Steve finds the dog still on the ship, we hear Cody bark, but his mouth doesn't move.
As Steve and Ned walk through the ship, after Steve surprises them in Jane's cabin, they walk past a white picture in which the camera is reflected.
During long dolly shot in the end credits, when Steve is walking left to right with the young boy on his shoulders, you can see the camera crew shadows pass in front of them several times.
Reflected in pictures as the camera passes through walls as characters travel from room to room.
On the deserted island, a red vehicle can be seen traveling in the background behind the hotel.
When Steve and Ned are in the helicopter, they're supposedly far out in remote "unprotected waters". There's a two-masted sailboat visible over Steve's right shoulder in several shots. In the same sequence, the water beneath the helicopter is shallow and churning with brown sand, indicating this was shot very near a beach.
During the film festival Q&A at the beginning of the movie, Steve Zissou needs a translator to understand questions asked of him in Italian. Shortly afterward, while in the adventure club with Ned, Steve can perfectly understand men gossiping about him in Italian from the next room.
Jane says she's reading a "six volume novel" to her unborn child, but is holding one volume in her hands while six others are lying on the chair, which makes it a seven volume novel.
Ned supposedly grew up in Kentucky, but he pronounces Louisville as "Lou-ee-ville". The locals pronounce it "Lou-uh-ville".
In the fax to Operation Hennessey alerting him of the alarm going off at the sea lab, Headquarters is spelled "Headquaters".