I have a lot of thoughts on this subject. If I was to make a blog entry on this topic, it would span multiple pages or have to be broken down into sub-topics.
I do think there is a correlation between good code and search engine rankings. I do not think there is a correlation between a w3c validated page and search engine rankings. The validator is not current enough, nor flexible enough, to accommodate the real world situations which websites encounter.
Example A: HTML 5 is recognized by all major browsers. W3C validation of HTML 5 is still experimental. A specific example that applies to SEO is the canonical tag. According the the W3C validation site, the canonical tag is not currently valid. Take a snippet of HTML5 code which passes validation, add a canonical meta tag to the header, and the code will no longer pass validation. This is a direct conflict between best practices and validation.
Example B: The world's most popular web page, google.com, does not pass validation. Matt Cutts discussed the topic. In short, they had a choice between providing code which validated, or code which worked. They chose to go with the working code.
Example
The standard facebook widget code, youtube video code, and other popular code does not pass validation.
Whenever I design a website, I check the code in the validator to look for errors. Initially, I will find numerous errors related to code outside of my control such as social sharing widgets or youtube videos. Once I remove that code, the page often validates. I have researched the issue and it is possible to modify the facebook code or youtube code so that it still functions and passes validation. Doing so requires extra effort, it provides absolutely zero benefit other then saying "hey, I pass validation", and there are often drawbacks such as having to add extra javascript to your site which can otherwise be viewed as unnecessary code.
1997 Jane Doe) for material to be copyright protected in the U.S. Once something tangible is produced, text, graphics, music, video, etc., it is automatically copyrighted."