"Windows Module Installer has stopped working" message constantly

That's (almost) OK :)
Here's the critical bit from the log...

Code:

POQ 133 ends.
2013-12-16 19:05:47, Info                  CSI    0000031c [SR] Verify complete
2013-12-16 19:05:47, Info                  CSI    0000031d [SR] Repairing 1 components
2013-12-16 19:05:47, Info                  CSI    0000031e [SR] Beginning Verify and Repair transaction
2013-12-16 19:05:47, Info                  CSI    0000031f Hashes for file member \SystemRoot\WinSxS\amd64_microsoft-windows-m..ttheme-de-component_31bf3856ad364e35_6.1.7600.16385_none_4d5bfdc5c9c70eda\DE-wp2.jpg do not match actual file [l:20{10}]"DE-wp2.jpg" :
  Found: {l:32 b:Ilj1k4TkbdWMV5xyLtXDGb5DYf2vLIJ6RIMRNlU/l4w=} Expected: {l:32 b:69jd9Ba0VnLK6zHIARf6z8E1eecFMrZ3N8UbxBn2EaQ=}
2013-12-16 19:05:47, Info                  CSI    00000320 [SR] Cannot repair member file [l:20{10}]"DE-wp2.jpg" of Microsoft-Windows-MarketTheme-DE-Component, Version = 6.1.7600.16385, pA = PROCESSOR_ARCHITECTURE_AMD64 (9), Culture neutral, VersionScope = 1 nonSxS, PublicKeyToken = {l:8 b:31bf3856ad364e35}, Type neutral, TypeName neutral, PublicKey neutral in the store, hash mismatch
2013-12-16 19:05:47, Info                  CSI    00000321 Hashes for file member \SystemRoot\WinSxS\amd64_microsoft-windows-m..ttheme-de-component_31bf3856ad364e35_6.1.7600.16385_none_4d5bfdc5c9c70eda\DE-wp2.jpg do not match actual file [l:20{10}]"DE-wp2.jpg" :
  Found: {l:32 b:Ilj1k4TkbdWMV5xyLtXDGb5DYf2vLIJ6RIMRNlU/l4w=} Expected: {l:32 b:69jd9Ba0VnLK6zHIARf6z8E1eecFMrZ3N8UbxBn2EaQ=}
2013-12-16 19:05:47, Info                  CSI    00000322 [SR] Cannot repair member file [l:20{10}]"DE-wp2.jpg" of Microsoft-Windows-MarketTheme-DE-Component, Version = 6.1.7600.16385, pA = PROCESSOR_ARCHITECTURE_AMD64 (9), Culture neutral, VersionScope = 1 nonSxS, PublicKeyToken = {l:8 b:31bf3856ad364e35}, Type neutral, TypeName neutral, PublicKey neutral in the store, hash mismatch
2013-12-16 19:05:47, Info                  CSI    00000323 [SR] This component was referenced by [l:180{90}]"Microsoft-Windows-LocalPack-DE-Package~31bf3856ad364e35~amd64~~6.1.7600.16385.LocalPack-DE"
2013-12-16 19:05:47, Info                  CSI    00000324 Hashes for file member \??\C:\windows\Globalization\MCT\MCT-DE\Wallpaper\DE-wp2.jpg do not match actual file [l:20{10}]"DE-wp2.jpg" :
  Found: {l:32 b:Ilj1k4TkbdWMV5xyLtXDGb5DYf2vLIJ6RIMRNlU/l4w=} Expected: {l:32 b:69jd9Ba0VnLK6zHIARf6z8E1eecFMrZ3N8UbxBn2EaQ=}
2013-12-16 19:05:47, Info                  CSI    00000325 Hashes for file member \SystemRoot\WinSxS\amd64_microsoft-windows-m..ttheme-de-component_31bf3856ad364e35_6.1.7600.16385_none_4d5bfdc5c9c70eda\DE-wp2.jpg do not match actual file [l:20{10}]"DE-wp2.jpg" :
  Found: {l:32 b:Ilj1k4TkbdWMV5xyLtXDGb5DYf2vLIJ6RIMRNlU/l4w=} Expected: {l:32 b:69jd9Ba0VnLK6zHIARf6z8E1eecFMrZ3N8UbxBn2EaQ=}
2013-12-16 19:05:47, Info                  CSI    00000326 [SR] Could not reproject corrupted file [ml:520{260},l:98{49}]"\??\C:\windows\Globalization\MCT\MCT-DE\Wallpaper"\[l:20{10}]"DE-wp2.jpg"; source file in store is also corrupted
2013-12-16 19:05:47, Info                  CSI    00000327 Repair results created:

I'd expected that one, because I don't have a German copy of Windows to extract the required file from.

I'm hoping (desperately!) that what we've done will be enough - or I'll have to download yet another copy of Windows.

Go back to Windows Updates and run a Check for Updates.... what happens now?
If/when updates are found, just try installing the oldest available update.

What happens? If it fails what error message do you get?

The affected file is definitely part of a German Windows install...
amd64_microsoft-windows-m..ttheme-de-component_31bf3856ad364e35_6.1.7600.16385
Note the version number is from the RTM of Windows 7.
Still - so long as everything else is OK, then you can probably live with it :)
If you start getting more problems, come back, and I'll work on fixing it.