Plot hole: How do they maintain communication between the ship at the centre of the earth and the surface? There's no wire, and radio waves can only travel any distance without obstacles, and the earth's crust would be a pretty hefty obstacle...
Plot hole: When the crew's vessel gets stuck in the giant geode and the crystal jams the 'impeller', the magma begins to fill the chamber. They see it melting the crystals, yet they frantically continue working to free the crystal from the impeller and lose a crewman...and yet when they get back in the vessel, the magma indeed melts out the crystal that jammed the impeller. With 2 geologists onboard you would think they'd know that.
Suggested correction: At no point do you see any of the crystals melting.
Plot hole: In the melting bridge scene, the space microwave was powerful enough to melt the bridge's thick metal but how come it could not melt the roof of the cars on the bridge? (01:27:10)
Plot hole: In the scene where they show how the earth's core has stopped moving and at the end of the movie where they show it moving again what instruments are they using to show these momentous events? According to the film, the inside of the earth is filled with various rock formations, huge diamonds and molten lava, not to mention intense heat, so what device(s) could sustain itself long enough to give back accurate readings?
Plot hole: When they come up with the idea of setting off the 5 bombs separately, there is a computer screen showing a picture of the Earth and the shock waves starting and interfering with each other. Each shock wave starts off from a different point - they are separated by at least 2000 km. But when they are dropping the bombs, they manage to drop them all within 2 hours (judging by the timer that they set on the first bomb). How did they manage to travel 10000 km in 2 hours?