The only thing I'd heard about The Core before watching it was that it has the worst science in any movie ever. Which it does. The Earth's core stopping, people traveling to it in a ship built with unobtanium, still being able to communicate with the surface through rock and lava, etc. But looking past that, it's a very decent movie.
The story is tight and gripping, much more so to me than other recent disaster movies, and the pace was great. Predictable in spots, but it's a disaster movie, what do you expect?
While the science is terrible, I find the concept to be fascinating, almost like a modern retelling of Journey to the Center of the Earth. When you look at it more like soft science fiction rather than a movie that's trying to be factual, similar to Independence Day, you can forgive the science blunders. At least they were trying for something different, rather than just doing aliens or asteroids, and they created something really unique. The effects also still hold up pretty well, for early 2000s standards, creating a visually appealing world, too.
The piece that really saved the movie from being B-grade was the acting. Aaron Eckhart, Hilary Swank, and Stanley Tucci give it their all, along with everyone else. Given that most of the movie takes place in a small ship that's travelling underground, everyone has to click with each other to get the right tension and atmosphere. Eckhart in particular has one scene where he's falling apart, screaming and crying, that was amazing.
Sure, it's not a classic, or even a 'great' movie, but it's not worth dismissing simply because "the science is inaccurate." If you're a fan of the disaster genre or any of the actors mentioned, I would highly recommend giving it a try.