redirect_mismatch

You should explicitly/manually set the Redirect URI in the Twitch.init call:

<script src="https://ttv-api.s3.amazonaws.com/twitch.min.js"></script>

<script>
  Twitch.init({
      clientId: 'YOUR_CLIENT_ID_HERE',
      redirect_uri: 'http://www.mydomain.com'
  }, function(error, status) {
    // the sdk is now loaded
  });
</script>

Of course be way about if your Twitch Application has a / on the end of the callback URL or not and update redirect_uri accordingly (for a while I was stumped as safari was being an ass and autocompleting the field with a / on the end)