if appropriate, should we tag questions with the name of the relevant command (eqnarray, align) as well as the general topic (equations) ?
I'd say yes, when there's a particular command that the question is actually about, rather than the principle or the kind of output. If a particular command only appears in an answer, even the accepted answer, I'd still be hesitant to tag the question with it.
I'm not convinced that this would be useful tag information. I would be surprised if there was anyone who specifically sought out questions on a particular command to answer (one use of tags is help people easily find questions that they might be able to answer). Similarly, anyone looking to see if someone's asked a question on a particular command before is far more likely to search for it than to look through the tags.
Of course, if there is a major command that attracts a lot of questions then I can see it might be appropriate (say,
\def, but even then I'd tag it "macros" since I see no reason to differentiate by tags between questions about
\xdef and so forth).
For any tag, the question has to be "Does this tag add anything to the question?". The key there is "add": if there's an obvious keyword already in the question, then the argument for having as a tag is weakened.
I must confess that I'm not a great user of tags, but what I find them useful for is to help decide whether or not a question is worth reading. On MathOverflow, if the title looks interesting but the tag says "algebraic-geometry" then I know that there's no point looking at it. On the other hand, if the title looks obscure but the tag says "differential-geometry" then I still take a look just in case the real question is more interesting than the title suggested.