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It's hard to tell exactly what you mean by dropdown menus ... I am assuming you mean for navigation? It depends on if the dropdowns are formatted so that a spider can read them. You can right click on the page from a browser and then view the source code. You should see URLs for all the pages you link to. If so, you've got no problems! If not, then you should use a different method to navigate.

I should have used the word purchase instead of conversion in my answer. I'm not sure Google gives any weight at all to conversions, since conversions are defined by site owners and not Google.

To answer your question, Christopher, if you use GA for ecommerce tracking it automatically tracks purchases, as well as custom conversion goals that you define. If you don't use GA on your site I don't know how they would know if a visitor converted or not, probably through pages per visit or other behavior that shows engagement with the site.

Other than on-site optimization, the main factors google uses for shopping results are things like bounce rate, conversion rate, time on page, etc. So basically if visitors are responding well to your products and making purchases, your shopping SERP will go up.

They are not nofollowed. The sidebar is automatically generated by the shopping cart so I'm not sure if I can nofollow them.

You'll be fine as long as your 301s redirect to the actual content and not to other 301s.

So 301 > homepage; 301 > homepage; 301 > homepage won't hurt you at all, but 301 > 301 > 301 > homepage will get you in trouble.

I run an ecommerce site with close to 2000 products. Nearly every page in the catalog has a too many on-page links error because of the navigation sidebar, which has several flyout layers of nested links. What can/should I do about this? Will it affect my rankings at all?

Thanks