Ah okay - that notice is definitely a factor then and an important consideration not initially mentioned.  So as long as you have someone else working on the other issues described then we can focus on the patterns concept I initially mentioned.

Several things that stand out when I'm reviewing links on a mass scale.I prefer to look at links grouped by domain in the first pass to help see these patterns.

1. Page titles of pages sending links.  Quite often, they're titles that blatantly scream junk/low-quality or irrelevant to any topic your site is about, or even link-partnerships... or even outright mention SEO.

2. Domain names/URLs of pages sending links. Same concept - they can quite often obviously communicate that they're junk, irrelevant, or blatantly specifically sites for SEO or links.

3. Anchor Text - if you group by anchor text as a next pass, look for links where the anchor text is exact match keywords and then look at the page title of that linking page and it's domain name.  Patterns can be spotted of low quality.  If needed, you can click over to a URL and just look at the page that  link is coming from.

4. After all that process, as you have marked links as being bad, regroup them by domain.  At that point you will likely still need to go through remaining links and go to at least one link from each domain to examine the page or just look at the overall domain for quality.

NOTE - the part where you examine a site sending links does require you to be able to know how to spot a bad site already.  Like - "Can I trust this site?" "Is this site obviously a fake site?" and other such questions need to be asked and answered.

And if a link is on a good site, is it a forum or blog comment?  Is it using an SEO relevant keyword as the person's signature name? Or is it even a legitimate and relevant comment, even if the link isn't using keyword anchors?

There are so many subtle indicators I could add but in reality the best way to go is to dive in and remember to look for patterns.  As you spend the time doing this work, patterns become more and more obvious...

Link schemes come in many forms these days.  Low quality directories are directories that are really just out there for people to get links for SEO value, and not really to offer high quality directory value.  Same with "bookmarking" sites.  Either they're really popular (like Reddit / StumbleUpon) or they're obviously just fake sites built for people to fake off-site SEO authority.

Link schemes can also include other scenarios.  Like getting links from a lot of very low quality sites - or even sites that have built some authority over time but are really just there for offering SEO links within crappy content.  Or where the content on those sites is so diverse as to cause the site to not have a cohesive topical focus.

And then there's "link wheels" - where one site links to another, and that other site links to a 3rd site, and that's the majority of links at least two of those sites have.

Evaluating links is a very time-consuming process.  You need to be able to look for "patterns" as a primary task IF you need to worry about links.

HOWEVER

I will also say this - your on-site SEO is suffering and just as likely or even MORE likely to be your primary problem. Why? Because you have not stated that you received a notice from Google informing you that your site was flagged for bad links.  If you did NOT get such a notice, while a poor overall link profile can certainly contribute to a generally declining ranking footprint, it's less likely to be the PRIMARY concern.

For example:  Your "Accessories and batteries" category has a terrible topical focus. The page Title doesn't mention what they're accessories or batteries for.  Which means from the very first point of reference on-site, that page fails to communicate the refined focus of the category.  Accessories could be about ANYTHING. And so could batteries.

Then, on that page, the header text "Accessories and Batteries" neither includes that topical clarification, nor is it even a proper "h1" header tag.  There's no descriptive paragraph based content on the page reinforcing and strengthening that topical focus.  Your Canonical tag is NOT SEO best practices for pagination in 2012, and thus that results in massive amounts of content within a category not properly being identified to further reinforce topical authority.  (You should instead be using rel-next/rel-prev and NOT using canonicalization on paginated content, every page title should be unique, and every page within a set should be properly reinforced with it's own h1 tag).

You're not even close to having enough depth of content on product pages (one sentence for the "detailed description), so with all the "related" . product content, sidebar navigation and other "off-topic" content, there's a lot of content on your site deemed "thin" content.

You have SEVERE page speed problems, a very serious SEO factor in 2012. (tools.pingdom.com reported a 9.3 second load time for the home page and URIValet.com reported 15 seconds).

I haven't even begun to scratch the surface here, because you have a SERIOUS on-site SEO problem that you've apparently either failed to understand or chosen to ignore in this question, which indicates there could be MANY more problems on the site.

Heck - several "minor" template fixes alone could boost your SEO, though if you really want to win, you'd be wise to really address all the high priority factors on-site.

Whether you have a site-wide link with exact match keywords, or even your design company's name, this is squarely in the "over-optimization" realm.  Created intentionally or not originally, it's now a best practice from an SEO perspective to eliminate site-wide links of any type pointing to a 3rd party site.

Hiding them with CSS is not recommended, as this too is potentially going to be seen as an attempt to fool people or search engines.

Purely from a "credit" perspective, if your clients are amenable to having a link to your site, it should either be on the home page footer, on the "About" page in the lower part of the content area, or another similar page.

If you have not been penalized for site-wide links, be aware that regardless of your or other people's experience at this point, it's on the radar for being targeted for its negative implications.