This question is about style and typesetting, but I believe it is more appropriate for this site than a TeX site.
When a bound is being established for some expression, it is not uncommon to see something like this: $ \begin{align} |\operatorname{Cov}(X,Y)|^2 &= |\operatorname{E}( (X - \mu)(Y - \nu) )|^2 = | \langle X - \mu, Y - \nu \rangle |^2,\\ &\leq \langle X - \mu, X - \mu \rangle \langle Y - \nu, Y - \nu \rangle ,\\ & = \operatorname{E}( (X-\mu)^2 ) \operatorname{E}( (Y-\nu)^2 ) ,\\ & = \operatorname{Var}(X) \operatorname{Var}(Y), \end{align} $ which I have pulled from the Wikipedia description of the Cauchy-Schwarz inequality.
The issue at stake is whether or not this is correct. Specifically, does a pedantic interpretation of $ \begin{align} a &= b \\ &\leq c \\ &= d, \end{align} $ necessarily mean $a = b$; $a \leq c$; $a = d$, or can we argue that the sane interpretation, i.e., $a = b \leq c = d$, is "standard" ... whatever that means.
I think I have let my bias paint this as a silly question, but it comes from a real debate, and there is a reasonable argument for using the interpretation that the aligned relation operators are a shorthand for carrying the left hand side implicitly to each line. If the inequalities are not strict, then you would always be safe using that interpretation, but that is not a good enough reason to adopt that viewpoint. An equality sign gives information about the nature of the simplification that has taken place on that line.
A proposed solution is to fix the alignment: $ \begin{align} &a = b \\ &\leq c \\ &= d, \end{align} $ and I guess this might be a good compromise. Certainly it is hard to argue for the commas that appear at the ends of the lines in the Wikipedia example.
A few minutes seaching in the library revealed examples of usage similar to the Wikipedia example in the works of Bourbaki, but even in France, some people don't regard Bourbaki as definitive.
So, I guess that is my real question: is there anything like Strunk and White for mathematics? Is there a definitive answer to the question above? If not, I guess this question should be CW.
Edit
Sometimes people have arguments about what is gramatically correct. This is a moving target, but there are at least certain "authorities" that might be consulted to resolve a dispute. Such disputes cannot usually be resolved by establishing that the sentence in question is unambiguous in its intended meaning, or that such constructions are overwhelmingly common in popular writing. For example, "The Cauchy-Schwarz inequality allows to bound the square of $\operatorname{Cov}(X,Y)$ by the product of $\operatorname{Var}(X)$ and $\operatorname{Var}(Y)$." (I made that up; I did not find it on Wikipedia.) The expression 'allows to' is not (yet) gramatically correct, but it is very common, and its meaning is clear.
The current question is in this vein. I think I can improve the question a bit. I have not looked for a specific example, but I expect I can find an example of a reduction of the form $a = b < c = d$ that is presented as $ \begin{align} a &= b \\ & < c \\ & < d \end{align} $
The intended meaning is again clear, and if that is all that matters, then there is nothing more to say. However, we cannot interpret this in the same way as the previous example. They are not compatible.
I think Qiaochu is correct that there is no authority that can be consulted here, so there is maybe no way for me to salvage the question, but I am hoping to at least show that the intended question is not any more innane than a question about gramatical correctness.
Is my last example actually wrong, or do we just admit that there is no standard interpretation for such a reduction; we are not machines, we are happy to get the intended meaning from the context?