First of all, congratulations for taking the initiative to write tests. There will be a Perl.com article that goes into more detail on this very soon.

I'm seeing the same results that you are. Let's take a look at the failures:

# test six
my $par = $doc->createElement('Paragraph');
is( $par->ownerDocument(), $doc, 'Element has correct owner');

not ok 6 - Element has correct owner
#     Failed test (t/docutest.t at line 18)
#          got: 'XML::LibXML::DocumentFragment=SCALAR(0x80b5b68)'
#     expected: 'XML::LibXML::Document=SCALAR(0x804b688)'
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Evidently the paragraph node is attached to a DocumentFragment. Setting the Paragraph as the Document's root element fixes tests 6 and 7, as well as the segfault and test 17:

$doc->setDocumentElement($par);
is( $par->ownerDocument(), $doc, 'Element has correct owner');
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As for the other tests, a little playing around got better results for me. Then I broke them again. I think you may be misunderstanding the DOM. I sure am. Maybe the libxml documentation will shed more light on the subject. Or mirod or Matt Sergeant will show up.