Windows installer fails to update itself with error 0x80073701 ERROR_SXS_ASSEMBLY_MISSING and will not load any other updates
Solution 1:
magicandre1981's suggestion in the comments worked:
Do an in-place upgrade to fix WinSxS issues.
magicandre1981 Dec 27 '14 at 7:26
After a year I figured it was OK to add your answer as the answer!