The truth is most SEO professionals use Validation errors as a way to say your site is not SEO friendly. I believe it is more of a sales tactic than anything else.
As with anything the basic answer is, "it depends". It depends on the location of errors as well as the type of error.
Assuming the validation errors are not semantic related, and most are not, it usually isn't the end of the world. More often than not the errors come from non-standard attributes or values in your CSS. This can happen if values are not read by some browsers but are by others and you need both in your CSS to make sure your site displays well across all browsers.
Googles homepage isn't even valid and as far as I can tell they don't read CSS for SEO.
If you want to spend time and money fixing all these you can but your budget for SEO is better spent on things that truly matter for SEO like the content of the page itself.