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Screaming Frog http://www.screamingfrog.co.uk/seo-spider/

I would start by cleaning up the on page. There is a lot wrong from ridiculously long title tags, no H1 tag, and missing alt and title tags on the images. A lot of the subheadings you use could be h2s as well. Also, don't forget to use internal links in the blogs back to other pages.

I would also make sure the articles you are writing align in content with what people are searching for.

Chain redirects just mean that a page redirects once, and then redirects again to something else.

An example might be a site that was originally in html, then php, and now has no file extension.

If the redirects were left in order each time a site was upgraded, you might go from page.html to page.php to page.

The easiest way to clean them up is to make sure all redirects go to the current version of the page.

I think you should look into the DirectoryIndex directive instead.

Normally a traffic drop like this is because someone failed to do 301 redirects of the old pages to new pages. I can't imagine the new site having enough technical issues or things wrong with on page optimization to cause the drop. It is also interesting timing, as the latest Penguin update happened recently, so the new site may not be the problem at all, but instead could be toxic links.

Took a quick look and the first thought is that you have no unique content on the pages, so they are likely being hidden by Google because they are duplicate content. This causes your main page to show instead, and not rank as well as the artist page, which is more targeted to the search term.

I would recommend awrcloud as you can set the location for your search and track different things like map results along with organic.

Could be that you used the same or mostly similar content on the city pages so Google isn't showing them. It also could be that your main product page is the one where all the links are pointing and none on the city pages, and probably in the menu or even the footer of this product page you have the city name pages linked as well and Google is simply weighting all the factors and determining the stronger page that may only show the city name once is more relevant than the city page which would be better optimized.

I'm sure you don't want to rewrite all the pages 1 at a time, try the following to rewrite the entire folder.

Options +FollowSymLinks
RewriteEngine on
RewriteCond %{REQUEST_URI} !(.)product
RewriteRule ^(.)$ product/$1 [L]

Just copy a couple sentences and paste them in Google surrounded by quotes. i.e. "content"

It depends on what you need. Some companies will have more experience in certain niches and be able to turn-key the linkbuilding since they know all the sites where you need to be. Others may be better in your local market since they will already know any local listings where you can get links and likely have contacts at the local newspapers and magazines as well. Just make sure the company has a strategy that they can explain to you before you start.

On top of Lesley's recommendations, both google and bing have url parameter exclusion options in webmaster tools.

Quick fix = do the redirects.

Best practice = do the redirects and try to get the inbound links changed as well.

It is best if you can get the links changed, but always be sure to do redirects as well as there may be other links that you are not aware of.

The larger the site and the more different kinds of areas to look through such as profile pages, blogs, forums, products, categories, etc will be more expensive as you have to check each for different types of problems.  You can probably glean a few improvements you could make yourself from SEO audit articles, our most recent is here: http://www.theedesign.com/blog/2014/seo-audit-design-doesnt-bring-you-traffic

Then of course there is:

http://moz.com/blog/how-to-perform-the-worlds-greatest-seo-audit

As an addition to what Tom has said, you should also setup parameter exclusions in webmaster tools to make sure pages with these appended parameters do not get indexed.

I would recommend Screaming Frog as well, but a couple free alternatives were recently mentioned in a YOUMOZ post, http://moz.com/ugc/conduct-a-backlink-profile-analysis-with-excel-case-study

I see it working now as well.  Also Spencer, if you ever want a good laugh go check out the H1s for the Moz Recommended companies.  I believe at least the first 5 on the page either have multiple h1s or none at all.

I can't even access your content on the site.  I see home, mobile, and desktop as text and when I click desktop it just highlights mobile again, so nothing changes.

The page in this case is /red, the #desc is a bookmark on the page.

Check out their learning section: http://moz.com/learn/local/local-search-data-us