During the breakfast scene, with each camera cut the cup Mora is holding switches hands.
At the end of the scene when Mora suggests to Johnny they go diving that day because of the full moon, Johnny turns and looks at the calendar. As the camera zooms in, we see the calendar has the phases on the moon on it. The camera continues to zoom to a tight shot of the calendar, at which point you can clearly see that the moon is simply a square of paper cut out and pasted over the regular calendar. The edges of the glued on image are slightly out of alignment, a couple spots the edges are curling up, and even the dark edges drawn on to match the lines of the calendar are ragged and bled over on the edge of the paper in a couple spots.
When Mora enters the water during the diving trip, the diving knife is strapped to her right leg. When Johnny and Mora are swimming together along the ocean floor, the knife is strapped to Mora's left leg. When Mora and Johnny arrive near the shiny object on the ocean floor, and begin digging at the reef, the knife is strapped back on Mora's right leg. The knife remains strapped on Mora's right leg until she removes it from the sheath.
In the scuba-diving scene, the boat in which Johnny and Mora are seen arriving at the dive-site has a dark-coloured, rounded lower hull, but the boat in which Johnny is sitting at the end of the scene has a flat-bottomed hull.
When Johnny sits and talks with Capt. Murdock in Murdock's home, directly behind the captain, stuck to the wall under a leopard's pelt, is a small photo of a seated woman. The photo is entirely unobstructed. As the scene progresses, the photo inexplicably moves several inches to the left, to where it is now half-concealed by the leopard pelt.
Sirens were not mermaids as stated in this movie, but were actually half female human / half bird, and there were only two or five of them depending on the stories. Mythology says that after Odysseus slipped by them, the Sirens dashed themselves onto the rocks, so none survived into the modern era.
Madame Romanovitch asks Johnny not to call her a fortune teller, as it's vulgar; she prefers to be called a cheiromancer or clairvoyant. But since she's reading the Tarot cards, she should more properly call herself a cartomancer, as cheiromancy refers to interpretation of the hands.
In the scuba-diving scene, neither Johnny or Mora are wearing any sort of timepiece such as a diver's watch which would surely be a necessity to determine the length of time they could stay under water.