The "science" regarding the interior of the earth is wrong, and was known to be wrong at the time the movie was made. It does not get cooler the deeper one goes into the earth. A few feet below the surface the ground temperature is around 50 degrees Fahrenheit. Going deeper from that depth the temperature goes up at a rate of approximately 1 degree Fahrenheit per 70 feet.
When some of crew go exploring on ahead, they keep in touch with the cyclotram by two-way radio. But most radio waves can't penetrate rock - you need to have a line of sight between the two transmission points. It is only recently that radios are being built that can send and receive underground.
Their ship called the "cyclotram" was supposed to be under 2500 miles of water. That is impossible because the pressure increases 165 time per mile one goes under water. That would mean about 6 million pounds per square inch. No hull could stand anywhere near that pressure.
The explorers stop tunneling at 1640 miles straight down. Considering their speed of travel and their angle of descent, it would take as much as two years to get that far. But we see no evidence that their trip takes anywhere near that long, and it's doubtful they could carry enough food and other supplies for such a long time.
The first time the crew exits the vehicle, the leader takes off his mask, takes a big breath, and declares, "The air is fresh and clear. You can take your masks off." But there could still be toxins in the air. In reality, they would have to use instruments to determine of the air was safe to breathe.
When the explorers first enter the cyclotram, it appears to pointed at the base of a mountain. But inside, looking straight ahead through the window, they see a neighboring volcano erupting. It would be impossible for them to see this from inside the cyclotram.
When the explorers are walking through the tunnels, their helmet lights are consistently pointed to high to do them any good.
Dr. Lindsey states animals born in the underground world are sterile but presumably the "first" rabbit litter they are waiting for was conceived by animals brought from the surface.
Early in the descent, just before they find the plaque, they are told they are 2.6 miles below sea level but earlier in the descent the 'depth gauge' was reading 3 miles.