Whatever book resides in the pantheon of grand literature defies dictionary-free reading, unlike one of those faddish, modern commercial novels.
This is a perfectly valid and grammatical sentence, and does make perfect sense. Can you please tell where you find the problem, especially the sub-verb agreement one? Knowing this will help me answer the question from the perspective of your confusion. And what is the source of the sentence?
Anyways, still I will give an answer.
I am now breaking this sentence like the following -
1. A = Whatever book resides in the pantheon of grand literature.
2. B = One of those faddish, modern commercial novels.
Now forming the sentence using A and B, it comes down to this form -
A defies dictionary-free reading, unlike B.
Though it's better to write this as following -
Unlike B, A defies dictionary-free reading.
Meaning - A and B are not alike. A defies dictionary-free reading.
Does my answer address your problem area?