Perhaps we could add to the question template that users see, a suggestion to mention the operating system or distribution, and also the version/release of that operating system. This should of course be only a suggestion, as this information is not pertinent to all questions.
Additionally, one could suggest that the poster mention the version of any software being used in the question, and also mention whether it is a binary package install or locally compiled.
While this would not apply to all questions, I think it would apply to a big chunk of them. However, perhaps I'm suffering from selection bias, because those are the questions I tend to answer. In any case, I seem to be constantly asking what distribution people are using.
A more speculative idea would be to customize the question template based on what tags people add, but I'm not sure how that would work.