When Olson and Bowen fight off the water dinosaur, Olson is firing an MP-18 submachine gun. As its name implies, it was not in service until 1918, two years after the film is set. Although technically incorrect, it's still a plausible weapon to use.
When the 'plesiosaurus' is attacking the submarine crew on top of the boat, and even kills and eats one, and it is trying to get Tyler, it has a huge head, but when it's killed and flops down onto the submarine deck, it's head and neck are much smaller.
In the opening scene with the U-boat, Captain Von Schoenvorts uses the designation SS in describing the ship he sees through the periscope. If it is a British passenger liner, the designation should be RMS; if it's supposed to be a British military ship, the designation should be HMS.
During the opening credits a sealed cylinder is shown floating in the ocean and eventually washed ashore. A sailor finds and opens it, retrieving some scrolls from inside. As he reads it, the cap changes between on and off the cylinder between shots.
(at around 45 mins) A group is walking on a hill behind a glass shot that has very little clearance. One crew member throws a duffel bag over his shoulder. As he does so, the upper portion is cut off by the glass painting.
Bowen puts his written account of Caprona into a German gas mask container and throws it into the sea - for it to be discovered years, if not decades, later. These containers were not designed to be water tight, and the pages would've been destroyed within days.