Other mistake: When they encounter the first ant, the policeman runs out of ammo, but the FBI agent fires at least nine shots. Not bad for a snubnose revolver that holds 5 or 6 rounds.
Visible crew/equipment: You can see the wires leading from the planes as they attack Gojira.
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.