I can't find anyway to view youtube comments. I can only see the description, the likes/dislikes, and related videos.
It's apparently not possible in the current version of the app. This may have something to do with Nintendo's policy of restricting unmonitored, user-generated content because of potential offensive material (which YouTube comments frequently qualify as).
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1Because Nintendo doesn't like "free chat". If they were to put in comments, they would be a post-only and come in a list of things to say like I like this, Or Good job! – The Idiot Gamer Oct 22 '14 at 1:57