The big limitation here is that what are known as adverbs and adjectives in English depend not on their spellings or syntax, but on how they function in any given sentence. For example, "running" is an adjective in "running dog" but a verb in "he was running." "Tomorrow" is an adverb in "we'll see you tomorrow," but a noun in "Tomorrow is another day." Word can't reasonably be programmed to distinguish these differences. Through grammar check, Word does some basic flags, say, when "slow" should be "slowly." But it doesn't know the verb "slow the car" from the adjective "the slow car." You could ask the Find function to highlight all words with "ly" followed by a space, which might turn up a small set of adverbs. But that's quite limited. (I've never gotten the "highlight all items found" to work--is this a known glitch?)
Anyway, maybe this helps explain some of Word's limitations in flagging parts of speech.