In addition to Jean-Guy's advice, ensure that your defined Table Styles do
not have "Do not check spelling or grammar" as a Language attribute as this
will cause the Spellchecker to skip them.
If this is not the case, check that this attribute has not inadvertently
been applied, this can happen after a copy/paste event. Select the whole
table (or the whole document to be sure), Review tab, Proofing group, Set
Language, make sure that a language is selected (regardless of specifics) and
that the two check boxes at the bottom are UNCHECKED.
Retry the Spellcheck.
Come back if required as it has been noticed that 2007 can have some
problems with spellcheck - table specific or not.
Hope this helps
DeanH