What's wrong with it, you ask? Well first of all, consider its length (frequently cited as a virtue). Concision may be a virtue in the right context, but it's not an absolute good. You need to consider your audience. This book imagines its audience to be beginning writers and so gives direct prescriptions (and proscriptions) in a dictatorial, ask-no-questions-I-know-best tone.
Even when this tone is relatively inoffensive, it conceals a great deal. The first two rules, for example, dictate how to form possessive singular nouns ('s almost always) and when to use a comma in a series (after every item except the last). Both are workable rules, but you would never know from Strunk and White that both have been the subject of debate, and that some other style guides give contradictory advice.
In a book addressed to beginners, of course, simplification is wise. There is no need for a novice to know about all the conflicts among different so-called usage authorities. But is this really a book for beginners?
The first eight rules all involve punctuation, and belong to a section labelled "Elementary Rules of Usage." What, however, is a beginner to make of rule 4:
"Place a comma before a conjunction introducing an independent clause."
That's clear enough, if you happen to know what independent clauses and conjunctions are. You say you can define them? Great, but rattling off a definition isn't the same thing as identifying them in real language. If you can, congratulations, but you're in a distinct minority. As I have discovered in years of teaching college-level writing and grammar-for-teachers courses, most students graduate from high school without having any real clue.
To identify independent clauses takes a moderate amount of grammatical knowledge, specifically knowledge about clause structure, and a useful description isn't something that can be encapsulated the three brief paragraphs (the space devoted to explaining this rule in my edition). And that's the problem. When Strunk wrote his first edition he could rely on the fact that his "beginning" writers would come to him with a significant background in grammatical terminology. His students would have spent years studying Latin. Today, few American high school students have much direct instruction in grammar. As a result, a book that once may have been usable by a beginning writer now requires extensive glossing.
Punctuation is usually assumed to be one of the most basic elements of writing, but it is only simple if you already have a fairly sophisticated understanding of phrase and clause structure.
There are plenty of other books that do a much better job of explaining what they mean, and do so less dogmatically, than Strunk and White. One good one is Martha Kolln's Rhetorical Grammar: Grammatical Choices, Rhetorical Effects.
Next time: Strunk and White's advice on word choice.