At the beginning, the meteorite is already on fire before it reaches Earth's atmosphere, and it continues burning even as it's sinking into the ocean.
An open diving bell cannot go very deep unless it is pressurised. For an open diving bell it would require increasing volumes of air to be pumped into it.
Without pressurisation, the air volume inside the bell would be compressed by the higher pressure water, causing the bell to partially fill with water. Eventually, as the bell continued to descend without pressurized air being supplied, the bell, and its occupants, would be crushed.
During the escape from Atlantis, the group is attacked by a swarm of flying fish (piranhas). Even though everyone is bitten, there is not even a scratch or some blood on them.
When the flying fish attack, Charles shouts "Coelocanths! They're supposed to be extinct!" Coelocanths are slow-moving, deep-water piscivorous fish. They would not attack humans, let alone fly out of the water to do so.
At 20mins in, they raise a gold statue some 10 ft tall. that size would weigh thousands of pounds and be too heavy for a couple of ropes and a block and tackle. the ship's deck might not even be able to support it.
The American flag flying on the ship at the beginning appeared to be modern, not 1896 vintage as the movie is meant to be.
The phrase "emergency backup system" wasn't in use in 1896, when this film takes place.
Charles is happy to go down in his diving bell with a large hole in it because it has an "emergency back-up system". When there is an emergency, he just rides it out.