The primary mission of a ballistic missile submarine is to hide and remain hidden. The aggressive chasing of an unknown target, which ultimately led to the crash, is completely out of character and most likely a direct violation of orders. They would be far more likely to have slowed down, so as to reduce their noise output and become more stealthy, then to try and sneak away.
The DeepCore crew had no idea what kind of triggering devices that Coffey had rigged to the nuclear warhead, nor would they have known how "vulnerable" or "touchy" he had made the bomb, so they would not have just randomly sprayed dozens of bullets around the Moon Pool in hopes of disabling Flatbed, since they might also hit something on the warhead and blow everybody sky-high.
Just before Bud touches down at the location of the warhead, his light flare is over 2 feet long, but when he touches down just a few seconds later the flare is burning out and is under 1 foot in length.
When Lindsey tries to open the door to the room where Coffey keeps the nuke, she is holding a fire extinguisher in her hands. Its visible side is just red. However, when Coffey opens the door, there is suddenly a white tag on it, as she is holding it with the other side on top.
The alien vehicle approaches the Montana on a course that nearly leads to a head-on collision. It is moving at 130 knots and the sub is moving toward it, yet it takes about 13 seconds for the range to close from 200 to 100 yards and another 3-4 seconds to come down to 60 yards, corresponding to a combined speed in the range of 13 to 20 knots. An object moving at 130 knots will go about 950 yards in 13 seconds, nearly half a mile (2025.37 yards in 1 nautical mile - 1 nautical mile = 1.15 statute miles or 1.852 kilometers)
Beanie The Rat does not produce visible air bubbles while breathing the oxygenated fluid, yet later, after Bud starts his fluid-breathing dive to the bottom of the trench, he is seen emitting lots of bubbles as he breathes.
The oxygenated fluid is a strong reddish color, yet in most of the shots of Bud's face as he is diving to the bottom of the abyss, the fluid around his face and head is either crystal-clear or only very pale reddish.
When they find the Montana, it looks like it's tilted (banked) to one side by about 50 degrees or so. A few shots later, it looks more like 70 or 80 degrees, and in the interior shots it looks more like 20 or 30 degrees.
When Bud and Coffey are fighting at the pool you can see a hand, on the right side, reach in and grab one of the dangling wires and pull it out of the way. This happens when Coffey, shown from behind, tries to stab Bud for the second time.
The Benthic explorer and crew are drilling for oil off the coast of Florida, where Cat says there is a pit 2-1/2 miles down. There is not a ridge or a trough anywhere near that deep near Florida, with Cuba "only 70 miles away," as the TV reporter said. The only trough even close to that depth is some 700 miles to the south of Florida, the Cayman Trough, which is even further south of Cuba and is closer to Jamaica than anything, and another ridge near Great Abaco, some 350 due east of Florida, both of which were not consistent with the Benthic Explorer's given location and the rig below it.
When the divers are swimming, you can see bubbles with every breath, meaning that they are on an open-system (i.e. scuba). However at that depth (2000ft), a standard scuba tank would be exhausted in under two minutes, or much less with any kind of exertion.
Judging by the way Virgil mounts the helmet and starts breathing immediately, the divers are breathing standard air. However, at that depth (2000ft) air would be instantly fatal, due to oxygen toxicity - not to mention completely impaired by nitrogen narcosis.
The divers are supposed to be at 2000ft, however this is twice the depth recorded using open-circuit scuba equipment, something that took weeks of planning, a large team of support divers, and caused severe HPNS (High Pressure Nervous Syndrome) in the diver.
Even if the wind force on the Benthic Explorer is enough to drag the massive rig along the seabed, it could never be enough to accelerate it from rest to at least 1 mph in less than a second when transmitted over an umbilical cord at least 2,000 feet long. No matter how strong the cord is, over that length it would have to stretch to some extent and this would limit the acceleration.
Ensign Monk tries to treat Jammer and says that he is "just a medic which is mainly about patching holes." SEAL medics have previous medical training before being trained as combat medics, and since they work with a scuba diving unit would also be well trained in any facet of diving related injuries and or maladies. So therefore he should have in fact had enough training to handle Jammer's malady.
Although, of course, all the equipment and terrain is fictional and only subject to fictional physics, it is intuitively extremely unlikely that something the size and weight of the fallen crane could pull something the size and weight of the rig along the sea bed, especially when the cable is draped over the edge of the cliff and the crane is presumably bumping along the rocky cliff wall.
Coffey states that the warheads on the submarine's missiles are "50 kiloton tactical nukes, about five times bigger than Hiroshima." Actually, Ohio submarines at that time were armed with 100Kt warheads. Any SLBM warheads then were considered strategic, not tactical. Also, 50Kt would be about three and a half times the yield of Hiroshima, not five times.
As an ultra-experienced military man, Lt. Coffey would surely have noticed the great difference in weight of his empty and "clip-less" pistol, no matter how ill or stressed-out he was. Even just an ordinary 6-chamber revolver is noticeably lighter without ammo.
Bud states that he is "the Toolpusher on this rig. When it comes to the safety of the crew there is him and then there is God". In fact, the Company Man has the top authority on a drilling rig. A Toolpusher is the highest drilling position from the drilling contractor side. The Company Man is an employee of the oil company that rents the rig and has the final word.
When the USS Montana crashes into the rock wall, it is clearly along its left (port) side. It then continues to scrape that side along the wall as they try to recover. However, when the Captain order his crew to surface he's told that all the Starboard (right) tanks have been damaged.
Coffey announces an oxymoron when speaking to his commander: "...could've been a Russian bogey." A "bogey" is a radar or visual contact whose identity is unknown. Thus, knowing that "a Tango and a Victor (Russian submarine)" were spotted within fifty miles, all Coffey had to say about the NTI incident was, "It could have been a Russian sub" or simply, "It could have been Russian."
While a defibrillator is of no use if a patient is truly asystolic, a patient in a "fine v-fib" rhythm can appear to have flatlined but still be revived with the paddles. Therefore, when in doubt, Advanced Cardiac Life Support guidelines call for administering the shock, though it's not the treatment of choice.
As Virgil descends into the abyss near the end of the movie, he is told he has broken the world record for depth. When he types his reply 'call Guiness'. Although Guinness requires two Ns, Virgil admitted earlier he was a bad typist. He also makes numerous other spelling errors during his descent.
Soon after Virgil begins his descent into the abyss, Linz informs him that he's broken the world record for the deepest sea dive. He smiles, which causes air bubbles to come out of his nose, even though he's supposed to be breathing liquid oxygen.
While Lindsay's drowning scene in the submersible was obviously played for dramatic effect, if they were really concerned about reviving her it would have made much more sense for her to take a deep breath and for Bud to then immediately began towing her back to the rig. She would have then drowned on the way there and there would have been less time between her drowning and the start of the resuscitation attempt, thus increasing the chance that she would be successfully revived.
When Coffey's submersible bumps into Lindsay's, she, Virgil and the submersible are shaken violently, however, the yellow rope coiled in the background remains stationary indicating the effect was achieved by shaking and tilting the camera.
When Coffey runs into the water tentacle and freaks out (just before he closes the door on it), the camera pulls back into a wide shot that shows the base of the tentacle coming out of the pool. You can easily see where the real water ends and the CGI begins as there's a seam clearly visible.
The goof items below may give away important plot points.
Cat says that "this here is a bottomless pit, two and one half miles straight down." That would translate to 13,200 feet. Yet, when Bud goes on his deep dive to disarm Coffey's nuclear warhead, Hippy nervously announces "17,000 feet!", which is nearly four miles down--and Bud had still not stopped descending.
Near the end of the picture, the alien "city" rises to the surface, carrying with it several sunken vessels along with the underwater rig. This of course implies that the vessels and rig were floating above the alien city as it rose from the depths. However, the rig was resting on a cliff edge and therefore could not have been lifted from beneath.
There is no possible way Lindsay could have survived the underwater swim, unconscious and without a breathing apparatus, let alone survived the hypothermia, during the sequence shown in the movie, which was when Bud towed her back from Cab 4 to the moon pool back at the rig. The brain can survive for up to about six minutes after the heart stops. If CPR is started within six minutes of cardiac arrest, the brain may survive the lack of oxygen. After about six minutes without CPR, the brain begins to die. Thus, there is no way for Lindsay to have survived the 15-20 minutes without oxygen, let alone not died from hypothermia, and even if it were possible for her heart to be started again, her brain would be dead and Lindsay would be in a vegetative state at best.
Near the end of the picture, the alien "city" rises to the surface, carrying with it several sunken vessels. One of the ships, a freighter, is lying on its side with one of its propellers flexing and flopping from the wind (the ship, of course, is a model).