While the octopus Popeye battles often is depicted correctly with 8 arms, when Popeye is first "jailed" by its appendages, there are at least 12 distinct arms. After Popeye has dispatched the creature, the octopus is seen with a "hairdo" made up of more than 8 arms.
Popeye is shot up through the deck of Olive's boat by a cannon in the sunken ship. This is wrong in three ways: 1) a cannon's powder would not ignite to fire underwater. 2) The cannon fires Popeye at a 45 degree angle, yet he pops up through the deck of Olive's ship at a straight vertical. 3) Popeye's head goes through the boat's keel and all the way up through the deck, yet the boat doesn't sink and the deck hole disappears by the next scene.
Popeye and Bluto wear stylized diving helmets underwater, but they are not connected to any surface air supply or SCUBA tanks.
After a shark fights with Popeye, it ends up on a wall plaque with a sign that says, "Caught By Popeye With A Right Hook". It was actually a left hook by Popeye.