When they are about to set fire to fuel dumped in the Thames as Gorgo wades up the river, the wreckage of the Tower Bridge behind the monster can be clearly seen in one shot. But the bridge isn't destroyed by Gorgo until a few minutes after the fuel is set on fire.
At the beginning of the film, Sam is wearing a raincoat over his red sweater. A second scene shows him wearing the sweater only while moving to check on Joe. A following scene shows him removing the raincoat while moving forward to check on Joe.
When the ship lowers a bathysphere to look for baby Gorgo, the captain says the depth is 10 fathoms, which is 60 feet. But the height of Gorgo is later stated to be 65 feet. Gorgo was five feet taller than the water he was in.
The sailors put into port on what is supposed to be a small island off the West coast of Ireland. They encounter a local, and ask him a question, which he answers in Irish (Gaelic): "Cad a dhéanfaimid anois?" while gesturing in the direction they need to travel. This means, "What will we do now?" Anybody who understood this will wonder why he would answer in this way, until later in the film, when it gradually emerges that this is what he always says when required to utter a line that we are not supposed to understand. There is actually one occasion when the phrase used fits the situation.