Google has said many times that poor or invalid HTML validation doesn't impact rankings. Of course, web sites that don't work, a search engine cannot crawl. But if your site works but doesn't validate with HTML validation tools does not impact crawling, indexing, or ranking.
Google's John Mueller said on Google+ this week that poor HTML validation may impact other SEO related aspects, outside of ranking. John said it can impact "meta-tags, structured data, or link-elements (for example, if your hreflang markup isn't being picked up properly)."
He even gave an example:
In a recent example, a site was accidentally including a banner in the HEAD of a page. That might look ok in a browser, but it breaks the markup in the HEAD, causing us to potentially ignore the rest of it. A HTML validator can catch that for you. While validators aren't perfect, they will help you get closer to clean markup, which will make it easier to automatically extract your site's meta-data.Personally, I use the https://validator.w3.org/ when I need one, there are lots of other options too.
So keep this all in mind, as schema and these other implementations make more of an impact on your CTR.
Forum discussion at Google+.
