It's interesting that you apparently actually checked a validator to get the error count, and yet the two things you cite as errors are not errors, have never been errors, and are not listed in the errors returned by the validator. Both opening and closing tags for the html, body, and head elements are optional, in all versions of HTML that I am aware of (outside of XHTML, which has never been seriously used on the open web as it isn't supported by IE pre-9). There is a tag reported unclosed by the validator, but that's the center tag.
Anyhow, one downside to having syntax errors might be that parsers which aren't as clever as those in web browsers, and which haven't caught up with the HTML5 parser standard, might choke on your page. This means that crawlers and other software that might try to extract semantic information (like microformat/microdata parsers) might not be able to parse your page. Google probably doesn't need to worry about this too much; there's no real benefit they get from having anyone crawl or extract information from their home page, and there is significant benefit from reducing the number of bytes as much as possible while still remaining compatible with all common web browsers.
I really wish that HTML5 would stop calling many of these problems "errors." They are really more like warnings in any other compiler. There is well-defined, sensible behavior for them specified in the standard. There is no real guesswork being made on the part of the parser, in which the user's intentions are unclear and the parser just needs to make an arbitrary choice and keep going (except for the unclosed center tag, because unclosed tags for anything but the few valid ones can indicate that someone made a mistake in authoring). Many of the "errors" are stylistic warnings, saying that you should use CSS instead of the older presentational attributes, but all of the presentational attributes are still defined and still will be indefinitely, as no one can remove support for them without breaking the web.