Robert_Charlton - 3:23 am on Feb 7, 2013 (gmt 0)

From what I understand, the closer a page is to the root the better it is for SEO. So something like http://mystore.com/book1 has more SEO authority over http://mystore.com/cat1/author1/book1 given that there's no requirement to keep cat1 in the url.

This is conflating a bunch of different considerations... including PageRank drop in levels from home, directory structure vs link structure, hierarchical navigation vs flattened navigation vs "flattened urls", faceted navigation and duplicate content issues, and breadcrumbs... etc. It's not clear which you're asking about, but I suspect the whole ball of wax.

First, you're possibly confusing navigation structure with directory structure. They're not necessarily the same. Hold that thought for a moment.

"Flattening navigation", in general usage, describes a navigation structure that puts as many nav links as possible on the home page... thus, some feel, boosting link juice for SEO. Not true, as you're dividing available link juice among a greater number of links, and not prioritizing anything. For many people, IMO, this is an approach to avoid thinking about what a good navigation should be. The link-everything-from-home navigation structure doesn't scale very well, and a good hierarchical navigation structure is likely to work a lot better. That's my quick take on flattened navigation. I'll let someone else come back to nav structure later.

Your main concern, though, seems to be about faceted navigation and breadcrumbs... ie, about different ways of reaching the product page... which also comes about because of confusing nav structure and directory structure (aka folders).

I you have faceted navigation and you confuse your navigation structure with your directory structure (as many often do), that will result in dupe content, as you'll have different folders in your filepaths.

There has evolved a strategy of putting product pages in the root, independent of the navigation path, to permit faceted navigation while avoiding multiple urls, with different file paths, for your product pages. That, along with the breadcrumb issue, is discussed in this thread....

Choosing the best url structure
http://www.webmasterworld.com/google/4475535.htm [webmasterworld.com]

This best url structure thread isn't about flattened navigation, though. That's another whole other issue. It is one of the best discussions we've had on faceted navigation, though, and should help with many of your questions.