I am trying to check HTML 5 files for validity and have found the W3C validator. However I have found that this validator accepts grossly wrong HTML documents like this one:
<!DOCTYPE html>
<head>
<meta charset="utf-8">
<title>Hello World</title>
Hello
</body>
</html>
Here I have removed the opening html tag, and the opening body tag and the validator reports:
The document validates according to the specified schema(s).
I do not assume, that this document is anyhow compliant to the HTML 5 or any other HTML standard. Obviously the validator is not very strict, when it comes to nesting of elements or opening/closing tags.
Is there a more strict validator out there, which reports every tiny deviation from standard HTML?
But you are assuming that it isn't compliant. You could check by reading the standard.
See, for example, the html element:
While tool recommendations are off-topic for this site, there are no deviations from standard html in the code you've presented.
The Nu validator is very good at what it does.