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errno is sometimes read too late after the error: After another call
may have modified it. Here's a patch against py3k. Most of it or a
variant applies to 2.7 too, but I haven't really looked at that.
I've not looked at math code, where I don't even know what sets errno.
There might also be a late errno read at Modules/_ctypes/callproc.c
line 794: "space[0] = errno;". Does it want the errno from before
_ctypes_get_errobj()? I'm unsure what's going on there.
Modules/_multiprocessing/semaphore.c doesn't need the patch's extra
variable, it can instead be rearranged with the commented-out patch.

This stuff is hard to write automated tests for, hence there are none.
The patch is mostly straightforward: capture errno with new variable err at point of possible error when intervening calculation is needed before testing the value of errno. This seems like a good idea.
There is one relocation of memory freeing and the additions of
+ if (res >= 0)
+ break;
which I cannot evaluate.

Terry J. Reedy writes:
> There is one relocation of memory freeing
Modules/timemodule.c does '#if,if(..errno..)' after PyMem_Free(outbuf),
which can overwrite the desired errno. Instead of reading errno into
a temporary, I moved the free into both branches taken by the #if,if().
> and the additions of
> + if (res >= 0)
> + break;
> which I cannot evaluate.
errno is only needed after an error., so I moved 'res < 0' out of the
'while'.
 if (res == MP_EXCEPTION_HAS_BEEN_SET) break;
 } while (res < 0 && errno == EINTR && !PyErr_CheckSignals());
-->
 if (res == MP_EXCEPTION_HAS_BEEN_SET) break;
 if (! (res < 0)) break;
 } while (errno == EINTR && !PyErr_CheckSignals());
-->
 if (res >= 0) break;
 err = errno;
 if (res == MP_EXCEPTION_HAS_BEEN_SET) break;
 } while (err == EINTR && !PyErr_CheckSignals());

The patch seems a bit confused at times. For example, you need to restore errno before calling PyErr_SetFromErrno().
Here is a new patch for py3k.

New changeset 6a966179c73a by Antoine Pitrou in branch '3.2':
Issue #10350: Read and save errno before calling a function which might overwrite it.
http://hg.python.org/cpython/rev/6a966179c73a
New changeset 8e0b2e75ca7a by Antoine Pitrou in branch 'default':
Issue #10350: Read and save errno before calling a function which might overwrite it.
http://hg.python.org/cpython/rev/8e0b2e75ca7a 

Committed in 3.x. I won't bother backporting to 2.x. Thank you!