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[Added OpenBSD Python port maintainers to the nosy list.]
I've identified a number of tests that all pass when Python is compiled
without threads, but fail otherwise. The failures are probably caused
by libpthread issues in OpenBSD, as described in this patch:
http://www.openbsd.org/cgi-bin/cvsweb/ports/lang/python/2.6/patches/patch-Lib_test_test_signal_py
Would you agree that it is reasonable to skip all these tests until
libpthread is fixed?

This looks reasonable. Perhaps you should add a reference to the relevant OpenBSD bug number(s) or URL(s), if any.

In addition to skipping the tests, would it also make sense to document these known limitations of Python threading on OpenBSD somewhere that end users might see it?

I can't pinpoint the exact causes for each individual test failure. I assumed that they are caused by threading/signal issues, because the tests pass when Python is compiled --without-threads.
But here's a list of possible culprits for future reference:
[pthread's execve(2) breaks close(2)]
http://cvs.openbsd.org/cgi-bin/query-pr-wrapper?full=yes&numbers=6183
[SIGCHLD handler is called at bad timing when linked to libpthread]
http://cvs.openbsd.org/cgi-bin/query-pr-wrapper?full=yes&numbers=6273
[pthread: 100% CPU usage after execv]
http://cvs.openbsd.org/cgi-bin/query-pr-wrapper?full=yes&numbers=6376
[pthread: file descriptors are "pseudo-blocking"]
http://www.mail-archive.com/misc@openbsd.org/msg80643.html
[test_siginterrupt_off broken by libpthread's internal hooking of signals]
[test_itimer_prof broken by libpthread's internal use of SIGPROF]
http://www.openbsd.org/cgi-bin/cvsweb/ports/lang/python/2.6/patches/patch-Lib_test_test_signal_py 

The FreeBSD-6.4-RELEASE-i386 buildbot has similar libpthread issues.
This is just in:
======================================================================
FAIL: test_send_signal (test.test_subprocess.POSIXProcessTestCase)
----------------------------------------------------------------------
Traceback (most recent call last):
 File "/usr/home/db3l/buildarea/3.x.bolen-freebsd/build/Lib/test/test_subprocess.py", line 770, in test_send_signal
 self.assertIn(b'KeyboardInterrupt', stderr)
AssertionError: b'KeyboardInterrupt' not found in b''
Re documentation:
Another approach would be to configure builds on systems with known
threading issues --without-threads by default. Advantages:
 a) Users will be immediately aware of the issues.
 b) Less work with the FreeBSD-6.4 buildbot.
 c) The --without-threads path is actually tested regularly.

The gentoo-3.x buildbot also shows the threading problems again:
test test_subprocess failed -- Traceback (most recent call last):
 File "/home/buildslave/python-trunk/3.x.norwitz-x86/build/Lib/test/test_subprocess.py", line 770, in test_send_signal
 self.assertIn(b'KeyboardInterrupt', stderr)
AssertionError: b'KeyboardInterrupt' not found in b''
References:
[gentoo-3.x]
http://bugs.python.org/issue4970
[freebsd-6.4]
http://bugs.python.org/issue3864 

All threading issues are fixed in OpenBSD 5.2.