Encountered the same issue with 3.1.2 and 3.1.3 64bit on Win7 64bit. I was able to fix it in registry but did so many changes at once that I'm not able to reproduce (was really annoyed after trying to fix it for half a day...). Anyway, sending my observations:

- the root cause seems to be creation of "python.exe" and "pythonw.exe" entries under HKEY_CLASSES_ROOT. Their open command did not have %*. They were not created under HKEY_LOCAL_MACHINE. They were probably created automatically by the system when manually associating py and pyw files (see below).
- .py and .pyw files were originally associated with py_auto_file and pyw_auto_file in HKCR. The associations were probably created by the system, when I manually change association of the .py and .pyw files from jython to python through control panel. The py_auto_file and pyw_auto_files seemed to call those python.exe and pythonw.exe entries in the HKLC.
- The assoc and ftype commands changed association in HKLM but it is not propagated automatically into HKCR, not even after restart. After manually deleting .py and .pyw entries from HKCR, they were replaced by correct entries from HKLM.
- BUT!! the system still called open commands under python.exe and pythonw.exe entries in HKCR! (even if .py was associated with Python.File in HKCR and proper Python.File existed even in HKCR!) Only after deleting them, it works as should. But I deleted a lot of other python related entries as well, so this is only assumption.

If anyone else can confirm that deleting of python.exe and pythonw.exe from HKCR itself corrects the issue, I think the installation program can check if these entries exists and offer to delete them.

Just for complete picture, it works now even with .py and .pyw in PATHEXT, so calling the scripts without extension.