I ran w3c validator with a 3.9.2 site and couldn't find any serious error that's a drama for modern browsers and ancient ones.

Only Plugin loadmodule creates "No p element in scope but a p end tag seen" because this module doesn't remove the <p> tags when inserting <div> containers which results in <p><div>...</div></p>. (BTW: Not that easy to correct this reliably without additional performance issues.)

If you find serious errors you should post and describe them more precisely here. Otherwise nobody knows what you are talking about and can decide if it's worth to spend time with it.

The bulk of these types of validation errors are going to be template specific, and on the configuration of the validator (it groans about HTML4 compliant structures which is a template level code change, or use of <meta> tags to fill in info for Google's structured data). The odds of there being a core level fix to make that 100% satisfies the W3C validator are slim to none.

I only encountered warnings with my 3.9.2 site. See images:
It would be wonderful if the checking gives you zero warnings and errors.

You need to set your template as a HTML5 template to make the type attribute warnings go away. The warnings in this specific case mean nothing more than a few extra bytes are being sent with the response by declaring something that is not necessary for an HTML5 document type.

Again, this is a template level change and not one for core to make.

It's best to contact the template making company. Thanks for pointing that out.

I'm closing the issue as it is not a core issue.