High five, happy to help!
What do I win? Just kidding 
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High five, happy to help!
What do I win? Just kidding 
Might seem obvious but I've seen pages being robots noindexed via meta tag at the page level, checked for that:?
Have you tried the Fetch as Goole tool in Google Webmaster tools?
Checked for crawl errors in GWT?
Submitted an XML sitemap to Webmaster Tools?
Is Bing indexing it?
Let us know how you go!
Did you implement 301 redirects from the old site, to the new?
Checkout:
Probably because it's relatively new. Just an idea, why don't you markup one of your own videos and run it through Google's Rich Snippet Testing Tool? Then you'll have a live example 
Is it a new link? You may have to wait till OSE's next update, which looks like it'll be on May 20.
See: https://seomoz.zendesk.com/entries/345964-linkscape-update-schedule
A very small amount IMO. Those that are:
Some sites serve different content to mobile devices, therefore require a seperate URL.
Google and Bing currently prefer responsive design because it allows the same URL to be displayed on desktop and mobile devices and requires less crawling ./ indexing on their behalf.
Agreed, it's not easy getting duplicate content indexed, and usually, that's a good thing.
Crazy Pills?
Nothing came up for 'Pimsleur' when I did an internal site search or a google site: search for that keyword on this site.
Might have been on another SEO site?
I'd think about the visitor experience. Are they finding what they're looking for via your existing search results for step by step recipes or would they be better served landing on a category page. Do you get a lot of search referrals using that keyword?
If you do decide to create a category page, add some unique content at the category level and build some links to it.
I guess my only reservation with that method would be that you say the enitre site is about step by step recipes. In that case, shouldn't you be targeting the homepage for that keyword?
2. If you do that you are going to dilute the strength / confuse the of relevance of the anchor text to that page. There is no good reason to do that.
I've used this for a number of clients. It is useful in generating a list of potentially harmful links and classifying them. However, you still need to manually review the results as sometimes there are false negatives.
If the blogger's sites are new/small/not well linked to themselves, it may take some time the mozbot to discover the links to your site. You should also consider the last time OSE was updated (Feb 12th 2013) and run another check the next time it's updated, looks like next update is set for March 12, see:
https://seomoz.zendesk.com/entries/345964-linkscape-update-schedule
Check a few things:
1. Length: Try and keep them under 70 characters
2. Content: Make sure they aren't spammy.
Either can trigger Googs to re-write your title.
What are you looking at charging?
You could try the free version of Rank Tracker: http://www.link-assistant.com/rank-tracker/
It checks Bing and Google and checks on demand, have a play and see if it suits your needs.
Nice one, now, if only someone could build a tool that would show / update the DA scores for each 
Sounds like a recipe for a duplicate content disaster, there would be nothing unique on the pages, just a list of jobs. Do not index those search result pages.
A couple more with high DA (over 50 the last time I checked) are:
http://www.hotfrog.com.au
http://searchsight.com
http://www.dlook.com.au
http://www.enterprisesearch.com.au
http://www.aubiz.org
http://www.comeonaussie.com
http://www.downunderindex.com
http://www.surfpacific.net.au
http://www.womo.com.au
I'm not suggesting using all of those for every client, but have a look and see if they meet your standards etc.