The trident of Atlan was said to have been forged with steel from Poseidon. In the movie, the trident was cast. Princess Mera continues using the term "forged" when relating the history even after seeing the broken mold.
When Arthur and Mera are fleeing Atlantis Arthur yells "Bogies on our 6" meaning hostiles behind them. The term for a confirmed hostile aircraft is "Bandit", "Bogey" is the term for an unknown aircraft, one that is shooting at you is definitely hostile.
When the Atlantean Soldiers come for Atlanna, when Arthur is three, she hands Arthur to his father. Arthur's hair goes from being short and curly to long and nearly straight then back to short and curly in the span of less than 10 seconds.
As Arthur and Mera are sailing away from Sicily, much of their dialogue shows them at the stern of the boat, with the boat's wake and the setting sun behind them. The final shot of the sequence, from behind the boat, shows it sailing forward towards the setting sun. The sun (or the boat) has changed location by 180 degrees.
When the Russian submarine is hijacked the pirates craft moors itself near the bow, presumable over or very close to the forward escape trunk. The majority of the submarine crew block themselves into the torpedo room, which is directly under the forward escape trunk. The pirates would have needed to go through the torpedo room to reach the command center.
During the flight over the desert, Aquaman and Mera appear in a DHC-4 or Caribou. In the real aircraft, the cockpit is above the cargo floor level; the pilot wouldn't be able to see his passengers the way it is shown in the movie. Also, the cockpit is much smaller than depicted in the movie.
In the 1985 segment of the movie, when discussing names for the baby, Tom suggests "Arthur" after hearing about the current hurricane Arthur on the radio. In 1985 the "A" named hurricane was Ana, in 1986 it was Andrew. Arthur wasn't used as a storm name until 2014.
In the very first scene, as the storm batters the coast, lighthouse keeper Tom Curry is securing a window shutter so it stays open. If anything, he should've been making sure all the shutters were shut to protect the windows from the forces of the storm.
If Arthur is impervious to "land made" metals, how did he get the scar above his left eye or, for that matter, get tattooed? During his youth Arthur was being trained by Vulko and was probably the one who provided the Atlantean metal to give Arthur his first tattoo. While the scar is the actors Jason Momoa actual scar from previous incident. Arthur could've received the scar from another Atlantean metal during his training.
The goof item below may give away important plot points.
The Sahara Desert has been a desert for 2-7 million years. Rome was founded in 752 BC. There is no way a message from "before the Sahara [actually] was a desert" could refer to a statue of Romulus erected in Sicily, which itself was not under Roman control until 241 BC.