The attached patch fixes a few problems with HTMLParser on 2.7.
Instead of raising error when invalid markup is detected, the parser now consumes the invalid input and proceeds.  This patch is a partial backport of #1486713.

After this two more patches will follow.
The first will get rid of errors raised while parsing declarations and should also solve #13576:
     def unknown_decl(self, data):
-        self.error("unknown declaration: %r" % (data,))
+        pass

The second will take care of "bogus comments" (see #13960).

Once this is done HTMLParser should be able to parse (almost) everything.  I'm planning to commit this before the release of 2.7.3.

LGTM, http://shipitsquirrel.github.com/

New changeset 11a31eb5da93 by Ezio Melotti in branch '2.7':
#13987: HTMLParser is now able to handle EOFs in the middle of a construct.
http://hg.python.org/cpython/rev/11a31eb5da93

New changeset 3d7904e3f4b9 by Ezio Melotti in branch '2.7':
#13987: HTMLParser is now able to handle malformed start tags.
http://hg.python.org/cpython/rev/3d7904e3f4b9

This should be fixed now.
The first two chunks of the attached patch have been committed in the two changesets linked in the previous messages.  The third chunk about the end tag has been fixed as part of #13933.  The error previously raised by unknown_decl has been removed in 4743a3a1e669.  More fixes have been backported as part of #13960.
2.7 should now behave like 3.2 non-strict.