There are many things violated principles of today's physics, but still maybe you can credit them to "sci-fi" title there. Yet, there are at least two basic ignorances that look silly:
1)To reach the core of earth, the vehicle must solve two problems: the extreme heat of inner part of earth and the tremendous power needed to propel the ship. The author "cleverly" solved this problem by "inventing a new material" that can absorb the heat and transform them into "pure energy" that propels the ship. This is a clear violation of the Second Law of Thermodynamics. A single heat source cannot creat work no matter what the media is. The author, by doing this, actually created an eternity engine.
2)If the above is a bit too "physics", then it is much more laughable while seeing the ship crews using radio to contact or signal their position to the base on surface. It is common knowledge that the water of ocean will cut the radio transmission off within a few meters. There is no way such radio transmission could reach the surface. If any communication was needed in that movie, the author should have thought about some other new "material" or methods, but he was too lazy to do the imagination work :).