Aggressive "answer" boxes. So you search for a question, and Google provides not just necessarily a featured snippet, which can earn you a click-through, but a box that truly answers the searcher's question, that comes directly from Google themselves, or a set of card-style results that provides a list of all the things that the person might be looking for.
In the zero-results sets, Google was still willing to show AdWords, which means if we have customer targets, we can use remarketed lists for search advertising (RLSA), or we can run paid ads and still optimize for those. We could also try and claim some of the data that might show up in zero-result SERPs. We don't yet know what that will be after Google rolls it back out, but we'll find out in the future.
Regarding Link Detox, links it diagnoses as Toxic are generally fine as they're either not indexed by Google or have malware/viruses/etc., but I recommend a manual review of any diagnosed as Suspicious. I used it recently to get started cleaning up our backlinks and some legit sites and blogs were under Suspicious simply because they didn't have many links pointing to them.
Organic is different. Matching keywords to user intent means you may be present in many searches. The user may find you consistently, and once they get to your site, they are more likely to stay. Organic users are still your best long-term customers. In my experience, they have lower bounce rates and more pages visited, and they are more likely to return.
For our client: We were lucky enough to remove most from the prior agency outreach, we also went directly to many webmasters in which we wanted to remove links. We did not use the Disavow tool as it was not around when we completed this link cleanup, but we all know it has been said that if you are going to use the Disavow Tool to use it with caution.
So, you have downloaded your links profiles on a CSV and you now have an extensive list of all your linked domains. If you have been doing SEO for 8+ years like me you can probably just know from analysis which links are bad from a TLD and URL point of view. If you do not know too much you can use tools such as Link Detox: http://www.linkdetox.com/ to complete analysis of your link profile. I would always consult the advice of an expert SEO in this instance because it is easy for these tools to mistake good and bad links.
A variety of methods can increase the prominence of a webpage within the search results. Cross linking between pages of the same website to provide more links to important pages may improve its visibility. Writing content that includes frequently searched keyword phrase, so as to be relevant to a wide variety of search queries will tend to increase traffic. Updating content so as to keep search engines crawling back frequently can give additional weight to a site. Adding relevant keywords to a web page's meta data, including the title tag and meta description, will tend to improve the relevancy of a site's search listings, thus increasing traffic. URL normalization of web pages accessible via multiple urls, using the canonical link element or via 301 redirects can help make sure links to different versions of the url all count towards the page's link popularity score.
Google is moving into more and more aggressively commercial spaces, like jobs, flights, products, all of these kinds of searches where previously there was opportunity and now there's a lot less. If you're Expedia or you're Travelocity or you're Hotels.com or you're Cheapflights and you see what's going on with flight and hotel searches in particular, Google is essentially saying, "No, no, no. Don't worry about clicking anything else. We've got the answers for you right here."
Although it may have changed slightly since BrightEdge published its report last year, the data still seem to hold true. Organic is simply better for delivering relevant traffic. The only channel that performs better in some capacities is paid search ads, but that is only for conversions, not overall traffic delivery (Paid Search only accounted for 10 percent of overall total traffic).