Google Docs Viewer have problem in MultiSite sub-blogs

Only fix for 3.4.2 involves hacking a core file. The issue is already corrected in the upcoming version 3.5.

Edit wp-includes/functions.php. Around line 1810, you’ll find this:

'doc|docx' => 'application/msword',

Change that to this:

'doc' => 'application/msword',

The docx file extension is actually already handled properly later down in the file, line 1819:

'docx|dotx' => 'application/vnd.openxmlformats-officedocument.wordprocessingml',

So it will work properly once you remove the spurious extension.

Again, hacking core files is a bad thing, but seeing as the refactorization in WordPress 3.5 corrects the issue already, and there’s no way to do this in a plugin or theme or even with a proper drop-in, I think that this specific case might justify it.