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I would probably clean it up. Take that javascript code, put it in a new .js file and load it externally.

A 301 Redirect removed any duplicate content errors that were showing in the crawl report, maybe redirecting the old site to the new site this way would help.

I would include at least one main blog to your site. Not only are you putting out fresh new content on your website but maybe one day you will have a huge following of people interested in what you say in your blog. Blogs are great in helping your potential clients but sometimes really fun to read.

Do you have an editing software, or video graphic software to add a watermark? What about intros and outro's, even if it is just an image?

Personally, I think there is certainly some value in having a domain name with some age and would lean towards investing your money in that direction.  Your client certainly doesn't want to abandon getting some links to this page so I would encourage them to keep some budget open for that but if I had to recommend one over the other I think I would recommend getting the domain name with 9-10 years of history.

Good luck!

Is the brand name affected? Id make sure that you rank #1 for your brand name, because Google is giving those site large site links that almost go down to the fold before the #2 listing.

Also, I would grab as many social media profiles that you can, so if a user searches for you then your twitter, facebook, etc... accounts should show up on that first SERP page.

I'm sure there are a lot of different ways of getting rid of bad press(you'll find a ton of ideas here), and hopefully your company doesn't assume you'll create good press for them, that's up to them to change the ways they currently do business for the future.

What you are referring to are site-links. I find that they appear mainly when searching for a brand name, hence when you searched for SEOMoz, you saw those site-links. But if you searched for "seo", you will notice that they are not as dominant.

Also, they are generated by Google. You can go into webmaster tools to remove them (and kind of strategically select which ones you want to appear) , but you cannot create them yourself.

We use hyphens and non-hyphen keywords for seo. We have used it for quite some time and we have seen no negative effects.