Please see http://docs.python.org/genindex-T.html

  Thread (class in threading), [1]

This two links point to same place. I think latter should point
http://docs.python.org/library/threading.html#thread-objects
or
class threading.Thread(group=None, target=None, name=None, args=(), kwargs={})
bellow.

# Latter doesn't have perma link.

You initial link 
I only see one entry, Thread (class in threading), which points to
http://docs.python.org/library/threading.html#threading.Thread
as it should. I do not see a duplicate link nearby.

I have no idea what ', [1]' is supposed to mean.

What does puzzle me is that

Thread [neader, no link]
   module

points to http://docs.python.org/c-api/init.html#index-64
it seems like the entry should have more. This entry is gone in 3.1.

> You initial link 
> I only see one entry, Thread (class in threading), which points to
> http://docs.python.org/library/threading.html#threading.Thread
> as it should. I do not see a duplicate link nearby.

It used to be there. Please see
http://docs.python.org/release/2.7/genindex-T.html
But ZipFile seems to have same issue, and still there.
Please see
http://docs.python.org/genindex-Z.html

>Thread [neader, no link]
>  module

Hmm, I cannot see this.

*Your initial post* only lists one index entry, and *does not* describe a problem.

Thread
   module

is in the file you have pointed to twice, in its alphabetical position.

I have no idea what you think is wrong with the z section.

Well, please see r85262 (10/6). This issue seems to be
recently solved in release27-maint. And http://docs.python.org/
was updated after that, so when I posted this issue, the issue was
actually there, but when you saw that site, (probably after
10/6, the issue was gone)

http://docs.python.org/release/2.7/
was created when officially Python2.7 was released,
so we can see this issue still there. Like time machine. ;-)

If I understand, the issue you were concerned about has been fixed. If so, please close this.

Yes, but http://docs.python.org/genindex-Z.html

  ZipFile (class in zipfile), [1]

still has same issue, no? [1] (and [2], [3], if exist)
should suggest alternatives, but it doesn't now.

I'll attach the patch to detect this kind of duplication.

I you say, probably this happens when same directive appears
in rst file. For example, 

.. module:: zipfile

.. class:: ZipFile

.. class:: ZipFile(file, mode='r', compression=ZIP_STORED, allowZip64=False)

Maybe I should have posted this issue to Sphinx tracker.

Umm, I tried, but I couldn't post new issue with error.
I believe Sphinx guys also look at this tracker.

When I initially wrote "I have no idea what ', [1]' is supposed to mean.
", you should have believed that and explained ;-). I now understand that most index entries have one link, which we might call the [0] link. When the entry should have more than one link, the index entry text is followed by '[1]' and, if needed, '[2]', '[3]', and so on. These place-holder labels should each have different links, or should not be there at all.

So "ZipFile (class in zipfile" and "[1]" are two separate texts that should have two different links, but the two links are the same, and that, I agree, is wrong. Another example with duplicate links:
  tracer() (in module turtle), [1]

3.1.2 and 3.2a2 indexes have Zipfile error but not tracer error (because '[1]' is not present).

Doc people: the attached patch is a diagnostic patch rather than a fixup patch. I do not know whether the problem is in .rst sources or Sphinx.

Georg, do you have any idea what the source of the index glitch is?

It is indeed what Hirokazu suggested: there were two ".. class:: ZipFile" entries in the docs.  I've added ":noindex:" now to one of them in r86425.