The problem with much science fiction is the dryness of the writing style. This is true also of Arthur C. Clarke's other works (Yes, even '2001'). Character development is often clunky and sometimes laughably naff. The thing to be appreciated in them is often the concepts and stories, ie. a paraphrase would be just as good.
Here, though, the characters take a convincing central stage and really carry the story. The science bit is on a very small scale (conceptually, not physically!!). It merely involves a couple of ideas to raise the Titanic, but, frankly, this is not really the core element of the story.
Is the book dated? I don't see why reference to Mandelbrot and Titanic necessarily have to be, there use is fully justified in terms of the wider issues of the story.
Some people found the Mandelbrot bits a distraction from the 'story'. This couldn't be further from the truth. It is a 'B' story that successfully echoes the 'A' story, as is the intention with such a literary device. Both stories involve masters in their complex field, both who are ultimately, despite all the preparation and knowledge in the world, caught out by nature.
And this is the surprising parallel that ties the story together and teaches us an important parable, exemplified in the epilogue (which took me by surprise, in seeming out of place). Ultimately, whatever we do, whether Global Warming is our fault or not, however much we protect ourselves from it, the world will destroy humankind in the end. This is what happened to the Titanic and will happen to us.