Contempt was switched over to using an HTML5 doctype a while ago. I looked at the errors listed in the link you posted above, and they actually all look okay to me--while it is good to look for validation errors, not all new markup is going to match up exactly with the W3 standards specs at first (especially for things like HTML5). For example, here is an Open Graph protocol meta tag used for the Facebook Like sidebar widget which we recently added:
<meta property="og:tag name" content="tag value"/>
But the validator.w3.org link you sent returns an error for a line like that:
Line 36, Column 42: Attribute property not allowed on element meta at this point.
That error was triggered because property attribute isn't technically allowed by the spec. But in order to get the benefit the tag brings, we decide to use it anyway. There are several examples similar to this. When you read a validation report like the one you linked, you need to take into consideration what each item in the output means and whether it's proprietary but valid. It's a tradeoff to get extra functionality. What you really should be looking for in validator reports are things like syntax errors that will completely break the layout of a site or that are incorrectly nested elements.
With regard to HTML5, tools for web standards are still be getting worked out. I noticed the link you provided has a heading "Using experimental feature: HTML5 Conformance Checker." and it mentions that it may be unreliable a times. Just something to keep in mind when using validator tools like that one.
"The validator checked your document with an experimental feature: HTML5 Conformance Checker. This feature has been made available for your convenience, but be aware that it may be unreliable, or not perfectly up to date with the latest development of some cutting-edge technologies."
I also checked out your site. It loads quickly for me and works properly. The Contempt theme works well from what I can see, and it doesn't have any critical mistakes in it.