My rule of thumb is that "Errors should be fixed, warnings should be evaluated carefully". In particular, I recommend fixing any error that might break parsing the XHTML pages or the NCX TOC --- as they are the most common causes for a Reading System to "fail" loading the EPUB.
Note, however, that some errors/warnings might have popped up because epubcheck got progressively better and lately it started checking even the most hidden details of the specification, even if they completely (and safely) ignored by any (sanely coded) reading system.
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