I do* validate my pages, using the validator from W3C (haven't looked at others). I do not check for accessibility issues for the simple reason that I haven't looked into that subject.
The only other testing I do is just loading up the page and verifying that everything looks fine in the newest Windows versions of IE, Chrome, and of course Firefox.
And the point of validation? Well, to make sure your markup complies with the standards that any other web page should be expected to follow... which in turn means that any browser should be able to render the page properly. (All the major browsers do have their own quirky ways of interpreting improperly marked-up pages, but in theory, they should all interpret
proper markup in the same way.)
*Been a couple years since I've written a page, but replying anyway fwiw.
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