At one point Jonas threatens Heller stating that, since they're in international waters, he can assault him and get away with it. This is a common misconception. International waters are not lawless. Ships and ocean-based structures fall under the jurisdiction of and are subject to the laws of the country in which they are registered. Jonas would be held accountable for any crime committed at the research station the same way as if he committed it in the United States (assuming that's where it was registered.)
An on-screen caption indicates that the Mana One research facility is 200 miles off the coast of China. It is also built above the Mariana Trench, at the bottom of which is the hidden sea where the meg lives. The Mariana Trench is actually off the coast of Guam in the central Pacific, nearly 3000 miles from mainland China.
When Jonas is making his rapid descent in the submersible he starts getting a nose bleed and the crew monitoring his vital signs are alarmed at gas build up in his bloodstream.
He's in a pressurized vessel, rate of descent would have no effect on him physically.
It is mentioned that the nuclear submarine rescue attempt was in excess of 10,000 meters depth. The estimated crush depth of contemporary nuclear submarines is approximately 730 meters. Even making allowances for "classified" data on crush depth would leave any submarine well above the 10,000 meters mentioned. Of course, the movie is about a 70 ft shark from the Marianna Trench...
Owing to the general lack of sunlight at deeper sea levels, the Meg should realistically not be able to see at all as it surfaces, since the greater volume of light up there is much more overwhelming than what it's been accustomed to for millions of years. The book gets this right and has the important reoccurring plot-point that the Meg only surfaces at night because the sunlight hurts its eyes.
When Morris is in the boat with the helicopter, after telling the crew he called it in. When the helicopter drops the 1st depth charge, the water sprays before the depth charge is even close, 2nd the whale body would sink because it is "open" but when he is in the water after the boat takes off and he falls out, the helicopter light stays on him and you can hear the helicopter so couldn't they radio the boat to them he is in the water.
Radios don't work under seawater, except for Extremely low frequency (ELF) radio. But ELF only allows transmission of a few letters per minute and needs a gigantic (= country sized) antenna for broadcasting. In short, none of the wireless submersible communications shown is possible.
Dr. Heller takes a physical of Taylor and claims he is "in perfect shape." However, in the earlier scene with the Thai fisherman whose boat Taylor used to maintain, it was established that Taylor has been drinking non-stop for the past five years and this alcoholism has already impaired him to the point he is no longer fully functioning socially. Nobody is in perfect physical shape after that.
When the Meg chases Jonas and is caught by the cable attached to the ship, it can't reach him as he slowly paddles back underwater. Earlier the Meg easily pulled the entire ship backwards, so it would have no trouble catching Jonas. Even sheer inertia would make sure Jonas was within reach of the monster fish.
It has supposedly been 2 million years since the last Meg sighting. Such a discovery would prompt the world's paleontologists, scientists, etc. to keep it alive, as opposed to killing it. This is actually a major plot point in the novel.
The goof items below may give away important plot points.
When Dr. Taylor and crew first come upon the wreckage of the shark finning boat, you can see dead sharks with their fins removed floating among the wreckage. Sharks are negatively buoyant and without their fins sink straight to the bottom, which is an important plot point in the novel.
It would have been impossible to winch the shark tail first all the way onto the boat given the crane was located at the rear of the boat. And if they had actually brought the shark on board, at over 20 tons, it would have sunk the boat.
During the prologue Jonas claims to have "seen" the meg. This should not be possible as the meg was only released for the first time much later when the crew of Mana One break the seal of the gas that keeps the meg confined within its own sea-world.