It seems like you're trying to share something you believe is helpful, so I apologize if this comes off as overly critical, but that's really not a good tactic at all. First off, it's unnecessary. If you are fortunate enough to be able to isolate and redirect a page with bad links (as you said, assuming there aren't good links in the mix), then you'd do just as well to 404 that page entirely. There's no need to redirect it somewhere.

Second, it could actually look manipulative. Redirecting a page full of bad links to a 3rd-party site would look to me like negative SEO. I have no proof Google penalizes this particular behavior, but it seems like a red flag that could potentially cause risks for the site setting up the redirects.

Even if the risk of that happening is <5%, it's a risk on top of doing something completely unnecessary. Just kill the page (404 or Meta-Noindex if it still has user value) - it's a clear signal to Google. If you start getting weird with 301-redirects, you could raise alarms.

As best we know, 404s should kill the page as a link target, which essentially severs the links. I don't think Google views the link on a domain-wide level at that point. If they did, then honestly it's likely the same rules would apply to other HTTP headers, including 301s. If the page is dead, you're pretty safe at that point. I don't think 301-redirecting the bad page is going to have any additional positive impact.

Re: "breaking rules", the problem is that it's very subjective. Let's say that a bunch of SEOs realize that Penguin and other link-based penalties created an opportunity, and they start taking their own pages with bad links and 301-redirecting those to competitors (maliciously). If Google sees that pattern and then they see you 301-redirecting your links to a 3rd-party site, they may not be able to separate you from the pattern. In other words, they're going to assume bad behavior.

That's speculation, of course (in this specific case - I've definitely seen them mistake bad intent in other areas). I just don't see that you'd be gaining anything by taking on that risk, even if it's small.

It's a trade-off, for both SEO and users, and I don't think there's one answer that fits every situation. The category level can add information, but it also makes URLs longer, which can be bad for both bots and people. If you have short, descriptive categories that aren't repeated in the product/page names, and those categories mimic your site structure, then I think it can be positive.

My argument was mostly against people adding categories just for SEO benefit (it's probably minimal, at best) or repeating every category, sub-category, etc. to the point of absurdity, causing keyword cannibalization and massive URLs. For example:

www.bobscamerashop.com/cameras/digital-cameras/canon-cameras/eos-cameras/camera-canon-eos-rebel-t3

Of course, that's also keyword stuffed, but I'm exaggerating to prove a point. You can go too far in either direction.

In general, though, I don't think categories in the URL are necessarily bad. In some cases, as Woj said, they could be a positive for users and possible even SEO.

Unfortunately, the painful reality, especially if you've been hit by Panda, is that you probably can't support that scale or that it looks thin to Google. 500 cities X 50 categories = 25,000 "category" pages, so to speak, all of which are basically just search results. For most sites, it's just too much.

I'd definitely keep the cities as sub-folders. If you go the sub-domain route, you could fracture your internal link-juice even more. It depends a bit on the authority and marketing budget of the site. If each city is a separate property with its own sales force, budget, etc., there may be a logic to sub-domains. Unless you're Groupon or someone like that, though, it's probably a bad idea.

You may have to prune down the indexed content, to be frank. I'd look for other Panda factors, too, like aggressive ad density (too many ads to too little content) or very thin pages. If you have tons of cities or categories with no listings, META NOINDEX them. You could even do it dynamically - only let Google index a page if it has 1+ listings, for example.

I'd also take a look at other low-value content, like paginated search. If each city has 100s of pages and you're indexing page 2, page 3, etc., consider consolidating them. It's a tricky topic, but Adam Audette has a great write-up here:

http://searchengineland.com/five-step-strategy-for-solving-seo-pagination-problems-95494

These pages can look very low-value to Google. Add in search sorts and other variants, and your 25K categories could be exploding into hundreds of thousands of pages, before Google even gets to the listings themselves. The ads are the real meat of the site, and that's where you want Google to focus.

Oh, sorry - so these PDFs aren't duplicates with your own web/HTML content so much as duplicates with the same PDFs on other websites?

That's more like a syndication situation. It is possible that, if enough people post these PDFs, you could run into trouble, but I've never seen that. More likely, your versions just wouldn't rank. Theoretically, you could use the header-level canonical tag cross-domain, but I've honestly never seen that tested.

If you're talking about a handful of PDFs, they're a small percentage of your overall indexed content, and that content is unique, I wouldn't worry too much. If you're talking about 100s of PDFs on a 50-page website, then I'd control it. Unfortunately, at that point, you'd probably have to put the PDFs in a folder and outright block it. You'd remove the risk, but you'd stop ranking on those PDFs as well.

I think it's possible, but I've only seen it in cases that are a bit hard to disentangle. For example, I've seen a PDF outrank a duplicate piece of regular content when the regular content had other issues (including massive duplication with other, regular content). My gut feeling is that it's unusual.

If you're concerned about it, you can canonicalize PDFs with the header-level canonical directive. It's a bit more technically complex than the standard HTML canonical tag:

http://googlewebmastercentral.blogspot.com/2011/06/supporting-relcanonical-http-headers.html

I'm going to mark this as "Discussion", just in case anyone else has seen real-world examples.

I haven't seen this solution in play, but I'd be cautious. It's a bit gray, at best. Google is okay with AJAX-driven menus, for example, and often won't crawl them, but this adaptation of HTML5 is kind of cheating the attributes of a link, and that could get you into trouble. Google may just outright crawl them anyway.

Truthfully, the data on mega-menu usability is really mixed. People often find them much less useful than webmasters and business owners think they are. Many people never see them at all. I think  you should really consider your information architecture and whether even having mega-menus is useful. When you make everything important, each thing becomes less important, both for people and for Google.

Unfortunately, other than being 99% sure there was an algorithm update around May 9th (dubbed "Phantom" by some folks), and even having seen it hit a former client, we have very few clues about what it actually did. Some folks have suggested it was "Panda-like" in which case thin content could be a culprit.

It's really tough to tell without seeing the site and the scope of the problem, but doubling up all of your rental pages could absolutely create problems, especially when you pair that with geographic searches and drill-downs. A couple of things I'd dig into before you completely change your structure:

(1) What's the scope of the doubling up, relative to your entire index size?

(2) Are there other culprits, such as search sorts and filters in play?

(3) Have you managed pagination (most likely with rel=prev/next, but there are other options)? With all of these geographic folders, you might have a ton of paginated search.

I think reducing your index size could be beneficial, but I'd make sure that the rental pages are the primary culprit first. I don't think the property URL change would help that much. It's a nice-to-have, but it wouldn't impact Panda or cause you major problems with Google the way it is. It's just slightly less user-friendly and slightly less keyword-targeted. I'd deal with the thin content first.

One thing I'd keep in mind is that a lot of your main nav pages aren't always great landing pages for search users. "About Us" is a decent landing page for finding out about your company (and that or the home-page should rank fine), but it and "Contact Us" aren't usually good bets for your non-brand keywords. It's often better to have a dedicated page targeting separate services.

I think it's fine to use keywords for the "Services" page, or you could split that page into specific services. Then, each service would have a keyword-targeted internal link and content. In that sense, think of your services like products - you branch from a main "store" page to categories to individual products. Done well, it serves both users and SEO.

I'd tend to agree - this used to be a bigger deal, but as IPv4 space runs low and more and more sites share IP addresses, Google has had to be more forgiving. I'm slightly concerned that the 20 domains are all duplicated, though - that could start to look like a link network. If it's just one site and you have a solid link profile, it's probably no big deal. In most cases, Google would just filter those links and they might even filter the domains (basically, they'd be ignored). If you're seeing this situation repeat itself, though, that's a different matter.

I'm going to generally agree with (and thumb up) Mark, but a couple of additional comments:

(1) It really varies wildly. You can, with enough duplication, make your pages look thin enough to get filtered out. I don't think there's a fixed word-count or percentage, because it depends on the nature of the duplicate content, the non-duplicate content, the structure/code of the page, etc. Generally speaking, I would not add a long chunk of "Why Buy With Us" text - not only is it going to increase duplicate-content risks, but most people won't read it. Consider something short and punchy - maybe even an image or link that goes to a site with a full description. That way, most people will get the short message and people who are worried can get more details on a stand-alone page. You could even A/B test it - I suspect the long-form content may not be as powerful as you think.

(2) While duplicate content is not "penalized" in the traditional sense, the impact of it can approach penalty-like levels since the Panda updates.

(3) Definitely agreed with Mark that you have to watch both internal and external duplication. If you're a product reseller, for example, and you have a duplicate block in your own site AND you duplicate the manufacturer's product description, then you're at even more risk.

Seems like you got the 301-redirect resolved below - if you've got that in place and fixed the canonical tag, it should be ok. It'll just take some time (usually longer than you'd like) for Google to clear out the pages, especially the deeper ones. If you see gradual de-indexation, though, you'll probably be fine.