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If it had a good reason to be there, and you had a decent link profile, then you are probably safe.  Even so, I'd say try to limit them to relevant pages.

The real question, though, is how much traffic is driving?  If it is driving a lot of good traffic that converts, then you pretty much have to leave it there.

I can definitely relate.  I work in the auto realm which is less trusted than the government according to a recent study.

Anyway, rather than just writing good content, go after viral content that people will share.  Maybe pull out an "Office Space" Esq campaign where you get even with office equipment.  Stapler vs hammer?  Monitor vs ground?  Projector vs office chair?  Printer vs a large amount of fireworks?

Then reach out to bloggers and humor sites to link back to your video.

I agree with Zora that by targeting the long tail you'll also optimize for the short tail.  To go further with targeting them all individually, that would depend on the competition, and the amount of variation of the keyword phrases.  Use the tools here on SEOMoz to find out the competitive level for those variants.  If it's pretty low, then one page would probably do, but if it's a tough search you would be better off creating more focused pages.

As for actually implementing a single page vs multiple pages, that would depend on context.  I would put "for sale," and "to purchase" on the same field, but clearance, to me at least, would be different.  If I were a consumer looking for a clearance product, I wouldn't want to land on just a regular page talking about buying the product.  I would want the page to match my search.

Contact a webmaster that could use the link juice, and sell all the extra websites to them for a hefty sum?

Even prior to reading that I would agree with your analysis.  2 links from separate domains are better than 2 links from the same root domain.

This article talks about a website that received the Penguin penalty, and was able to start recovering by reducing the amount of site wide links: http://searchenginewatch.com/article/2180722/Google-Penguin-1.1-Pushed-Out-As-Some-Sites-Report-Recovery

"A) Remove all of the crap sitewide links, weird anchors first, B) continue building good links and C) take advantage of press by pinging Danny Sullivan to try and get it featured on SEL to get in front of Google. Obviously A) was not going to be completely possible so I was going for "remove most of your crappy links."

So, I do believe that site wide links are bad, and that it would be better to limit the number of links.  Also, here is a reference about the diminishing returns on several links from one domain: http://www.seomoz.org/blog/understanding-link-based-spam-analysis-techniques

"The first link from a domain carries the first vote and getting additional links from one particular domain will continue to increase the total value from a domain, but only to a point. Eventually inbound links from the same domain will continue to experience diminishing returns. Going from 1 link to 3 links from a domain will have more of an effect than 101 links to 103 links."

1. To answer your first question, it does count all the links.  However, there is a massive diminishing return for anything over 2 links on one site.  So, having 1,000 links from one site would not be beneficial.  Instead, have them change it so you get one link on their top two pages, and none anywhere else.  You can use Opensiteexplorer.org and the top landing pages tab to find which two pages to request a link from.

2. A sub-domain is a separate site, and would therefor have its own ranking ecosystem.  Even a www.abc.edu is a sub-domain of abc.edu.  So, getting a link from a sub-domain would be as beneficial, everything else being equal, as getting it from the root domain.   Just make sure it's just a link or two, and not site wide like you suggested you currently have.

Depending on the tool you use, you should be able to see the density of phrases, as well as specific words.  However, keyword density shouldn't be your main focus.  You should consider the overall contextual relevance of your content, as well as the readability.  By focusing purely on density you could find yourself getting over-optimized.