In the scene where Kathryn is falling down the waterfall, you can clearly see she is only wearing her dive booties. But as soon she enters the water again she has her fins on.
When Briggs is talking to the rest of the team on the fiber optic line, the counter on the video screen jumps backwards between shots.
Several scenes show the explorers using their HID (High Intensity discharge) dive lights out of the water. HID lights use the surrounding water as a coolant and thus cannot be used for long periods of time above water as they would heat up too much and croak.
When Strode's DPV (diver propulsion vehicle) explodes, there is a fireball. DPVs are electric, so there is nothing to ignite into a gas-like explosion.
The characters seem to have completely normal uninhibited conversations under water despite having a mouthpiece fully inserted into their mouths.
When Charlie is climbing the rocky wall, somewhere near the end you can clearly see her taking her palm from a climbing hold bolted to the rock .
Since a cave is a closed environment, you never use flares or any similar burning device inside a cave because it will fill it with smoke. That's a basic caving rule.
When asked if he is okay, one of the scuba divers gives the thumbs up signal while underwater. In scuba diving, thumbs up means ascend to the surface.
Tyler jumps into the water, then grabs his mask and puts it on and begins swimming, but he fails to clear his mask by blowing the water out of it. Without clearing it, he wouldn't have been able to see a thing.