When the Devil Fish attacks Dr. Bates, she trips and throws her ax overboard. Later, she picks it up off the deck, far from the side of the boat where she tripped.
At one point, Peter says the Devil Fish is eight feet away. A few seconds later, before it turns away, he says it's 20 feet away.
During the intro scene with the boat, the distant shot and underwater view show enough light to see the underside of the boat and land in the distance. Scenes on deck take place in pitch dark.
At time 1:10 when Peter knocks Stella over the side of the boat, the water depth is shown as no more than 6-8 feet deep. The depth is also shown much deeper than 20 feet in previous scenes.
At 44:53, the Seaquarium is shown dropping anchor, while at 45:50 the Seaqarium is shown under way, then moments later, at anchor again. All of this occurs while the crew is ruminating on coiling ropes, or having a beer.
An oil slick fire would do little damage to an underwater monster.
When Peter throws the beer can over the side of the boat to test the underwater scanner, it sinks far faster than possible.
As has been pointed out, Doctor Bates mistakenly says fish evolved teeth 320 years ago, presumably meaning 320 million and describing the devil fish as a toothed species from this era. However, the monster onscreen has a mouth that most resembles the maw of the prehistoric fish Dunkleosteus which evolved before teeth. The massive serrations in its mouth are actually part of its jawbone. The monster's very similar "teeth" also appear to be part of the jaw, not separate attachments to it.
At minute 23:00 all of the underwater scenes of the diver include a dark spot, roughly mid-screen.
At time 1:03 and 1:05 the engine sound of the Coast Guard boat is obviously dubbed in after the scenes were shot. The sound is actually that of an outboard motor, not that of a 900 H.P. Coast Guard cutter.
Dr. Bates says that fish with teeth developed around 320 years ago. She probably means 320 million years ago.
Janet continually mispronounces Cretaceous as "Cetaceous".
When looking at the buoy display, Stella says No. 4 isn't working, yet the red light for No. 3 is the one blinking.