Continuity mistake: When Richard Denning and Richard Carlson approach the boat ladder coming back from their first dive in the Black Lagoon, you can see the net hanging underwater just to their right. It already has the huge torn hole that is in it when they hoist it up after the creature is caught for a moment in a later scene.
Continuity mistake: When the scientists find the creature climbing onto the ship at one point, it's night time. It smashes a lamp, then jumps back in the water, swims across the lagoon, then standing up near the water's edge, it grunts and slashes at the spotlight they aim at it, then goes back underwater. Two of the scientists dive in to go after it, and follow it through an underwater (then above-water) cave. When both creature and scientists exit the cave, however, it is not only daytime, but the other scientists are waiting on the shore nearby.