These are correct as they are:

Lib/tkinter/tix.py:149:        """Locates a bitmap file of the name name.xpm or name in one of the
Lib/tkinter/tix.py:160:        """Locates an image file of the name name.xpm, name.xbm or name.ppm

Modules/_io/iobase.c:79:    "Change the stream position to byte offset offset. offset is\n"
<I believe the 2nd and 3rd 'offset' are argument names, which would be specially marked in .rst>

Modules/socketmodule.c:3547:           ensures that that doesn't happen. */
Modules/binascii.c:41:** I have attempted to break with this tradition, but I guess that that
Doc/c-api/intro.rst:436::c:func:`sum_sequence` example above.  It so happens that that example doesn't
<'that that' is awkward, but the two 'that's are different>

Modules/posixmodule.c:9747:Return the value of extended attribute attribute on path.\n\
Modules/posixmodule.c:9825:Set extended attribute attribute on path to value.\n\
Modules/posixmodule.c:9890:Remove extended attribute attribute on path.\n\
PC/msvcrtmodule.c:133:Create a C runtime file descriptor from the file handle handle. The\n\
<much like byte offset offset>

Doc/c-api/long.rst:206:   Return a C :c:type:`size_t` representation of of *pylong*.  *pylong* must be
<the re missed the '.'.>

False doubles from typos (which should also be changed):
Lib/test/test_socket.py:845:        # Try udp, but don't barf it it doesn't exist
/it it/if it/

Éric, I am puzzled by your comment. The only two 'the the's in Serhiy's report (that Firefox finds) are

python-gdb.py:1466:        '''Is this frame "collect" within the the garbage-collector?'''
<I suspect 'collect' should be 'collected', but I cannot tell without a link. I am sure 'the the' is wrong.>

Misc/HISTORY:3055:  environment after Distutils set it.  Instead, have Distutils set the the

and both look like wrong doubles and not 'that the'.