This is related to another question I recently asked about storing a non-bare repository in Dropbox for easy movement between computers, so it may be helpful to read that question for background.
The gist is that the fileMode keeps reporting a diff for some number of files. I can't find a way to reproduce it consistently, but it happens frequently. What I've noticed is that the file, which has 644 permissions on both machines often reports a diff from 755 on one of the machines. This makes me think that Git believes the executable bit is set, but I can't figure out whether I can actually see how Git has that bit set.