You could try searching NerdyData for a search operator like below:

href="http://example.com

Make sure to leave the closing quotation mark out to account for any sub pages.

This may or may not  return some different results, it's worth a shot.

I would tell your client to not worry about it.  I didn't know that GoDaddy was in the SEO consulting business now?

I found this as an explaination of what a GoDaddy SEO Checklist Stop Word means:

Words that are common do not help search engines understand documents. Exceptionally common terms, such as the, are called stop words. While search engines index stop words, they are not typically used or weighted heavily to determine relevancy in search algorithms.

It sounds like more of a warning to me.  I wouldn't worry about it.

To 301 redirect all files in the direct to the new directory in .htaccess, try this:

RewriteEngine On
RewriteRule ^old\ foldr/(.*) /newfolder/$1 [R=301,NC,L]

This should redirect all HTML pages, images, you name it.  It should also account for the space too.

You'll want to move all your files to the new folder location so when the redirect happens your end user doesn't receive a 404 error.

I personally don't think it would make a difference one way or the other, as long as the proper 301 redirects are put into place and all traffic to the old URLs is sent to the correct new URL.

I do, however, think the sub-directory approach looks cleaner.  Anything beyond the first sub-domain looks spammy to me (or just sloppy).  That's just me though.

I don't think it's Google that is causing the problem, perhaps it's the browser.

In Chrome, I searched for your keyword.  I noticed the '%20' (the HTML character for a space) in the URL of the first result.  When I moused over the result, the HREF that showed had a space in the URL in place of the '%20'.  When I clicked on the result, it correctly sent me to your page, and did not replace '%20' with a '+' symbol - which can also be used to replace a space.

Have you tried writing .htaccess redirects to send users to the correct page if they encounter a situation where they are attempting to hit the + URL when they should hit the '%20' URL?

If the structure is identical (I'm not clear on that from your post) then why not do a global redirect from the old content to the new content

RewriteEngine On
RewriteBase /
RewriteCond %{HTTP_HOST} !newdomain.com$ [NC]
RewriteRule ^(.*)$ http://newdomain.com/$1 [L,R=301]

This should redirect old pages to the same structure on the new domain, including images.

I understand what you are referring to about having to hide certain elements on smaller screens.  Sometimes not everything fits or flows correctly.

When this happens, however, I try to hide design elements as opposed to text or links.  I'm also OK with hiding images.  If a block of text or a link seems out of place or doesn't flow properly, I will build a dropdown for it.  I'm sure you've seen mobile sites with dropdown navigation menus.

I wouldn't leave it to up to Google to interpret what you are doing.  Don't hide any links.

The thing is though - these methods will not increase your rankings.  Google has pretty much devalued any links that we have some form of control over (directories, forums, blog comments, social bookmarking sites - even guest posting).