On: This website has a lot of unclosed h3 tags

[brokenparser]

Renders perfectly in IE4, too.

[grahamel → brokenparser]

Seems like it's IE being a bit loose with the spec (the doctype is html 3.2 after all) or just catering for the likely hood of a rule for one element being used for another.

For headings, on http://www.w3.org/TR/REC-html32#headings it says "You always need the start and end tags" but for block elements underneath it says that:

    <P>This is the first paragraph.
    <P>This is the second paragraph.

is perfectly valid - presumably why it's fine in IE8