Its a bit technical but you can go through this https://developers.google.com/webmasters/ajax-crawling/ to make sure the dynamic page that you generate is actually indexable by Google.

That said 5000+ products infinite scroll is a bit scary and I would look at using rel=next and rel=prev for the pagination ( http://googlewebmastercentral.blogspot.com.au/2011/09/pagination-with-relnext-and-relprev.html )

I am not too sure what you mean by " internally linked to from the browsing results pages in the category structure: e.g. Blue Widgets, Widgets Under $250, etc. "

If you are referring to ability for users to sort through those products by picking one of the options like Blue Widgets, Widgets Under $250, etc. I would suggest rel canonical those pages to the base page . This should get you started http://support.google.com/webmasters/bin/answer.py?hl=en&answer=139394

It's most likely because some one would have put a DMCA takedown on that Google search result. jump in to your Google WebMasterTools account and you should see some notification from Google about it.

I would not worry about multiple H1 as a major issue .( as long you are not over doing it )

MattCutts :

http://www.youtube.com/watch?v=GIn5qJKU8VM&feature=player_embedded&noredirect=1

Personally I would index comments but have a nofollow attribute to links within the comments. See what sort of tile and description the comments url generate ( you dont want duplicate titles and meta for those )

EDIT:

do you have some sample urls we can look at ?

Not trying to throw a spanner in the works, but have you considered top level country specific domains ?  .co.uk, .au, etc

In theory you can use subdirectories and  assign geo targeting  for that folder in Google Webmaster Tools. ( keep in mind this will only work for Google, you have to look at how the other search engines will handle this Bing, Yandex if you target Russia, Baidu for China, etc )

You can use some of the tools here to personalize content on your landing page, that said Google will try and rank you for the content it sees when they crawl the site. You can try and see what they see using The Fetch as Google tool from Search Console.

Targeting Monkey

When it comes to subdomain vs subfolder, SEO's usually prefer to go subfolder. But if it's easy and financially suitable to go that way I would say go for subfolder. In this day and age the SEO impact is minute ( if any )

Matt Cutts's view ( Oct 2012 ) : http://www.youtube.com/watch?feature=player_embedded&v=_MswMYk05tk