I can't really say how without including massive spoilers. So, spoilers aplenty from this point forth.
We think of Professor Moriarty as Sherlock Holmes' arch-nemesis. The first well-known supervillain in world literature. The funny thing is, Moriarty is much more prominent outside of Conan Doyle's stories than within them.
Moriarty only shows up at all in two of Conan Doyle's original Sherlock Holmes stories. (That's the same number of Star Trek: The Next Generation episodes that center around the Trek universe's version ofMoriarty. But nobody thinks of Moriarty as a Star Trek villain.)
What's more, for Moriarty's introduction, in 'The Final Problem', Conan Doyle performs a narrative trick that would have people rolling their eyes if someone tried it today. He doesn't bother to establish Moriarty as a supervillain at all; instead he just has Holmes show up and state that Moriarty's this evil genius. Moriarty's the greatest bad guy in England because Conan Doyle tells us so, not because of anything that we see him do.
Moriarty is famous, but when you go back to the source material you see that he is quite probably the most overrated supervillain in the history of fictional bad guys.
Nicholas Meyer probably wrote The Seven-Per-Cent Solution thinking much the same thing.
Moriarty is indeed very much in evidence in The Seven-Per-Cent Solution. He seeks out Dr. Watson and complains that Sherlock Holmes is hallucinating that he's this fabulous criminal mastermind, when in reality he's just a meek mathematics teacher.
Now, every reader is probably thinking at this point, Aha! Dr. Watson will of course fall for Moriarty's ruse -- but Holmes will see right through it and foil his plans in the end!
And every reader would be wrong. Within the universe of this novel, Moriarty really is a mild-mannered math teacher, and Sherlock Holmes is a crazed cocaine addict who's imagining things. (Told you there'd be spoilers.)
Nicholas Meyer spends the first half of the novel subverting and defusing Holmes' most famous antagonist. He has Holmes visit Sigmund Freud in Vienna, in order to receive treatment for his cocaine addition. Then he gives Holmes and Freud a case to solve together.
Now, if you define the 'plot' of a Holmes story to be the actual case that Holmes and Watson solve, then the plot of The Seven-Per-Cent Solution actually begins when the novel is more than half over. This may frustrate and annoy some readers.
On the other hand, Nicholas Meyer intends for the main plot to be character-based: Sherlock Holmes' journey from cocaine-induced paranoid fantasy to clear and sober thinking. In that respect, the book works much better.
I'm satisfied with what Meyer has done here, even if my expectations got a bad case of whiplash.