Comment 53 for bug 1651923

I have this problem still. What I found to work was to remove the failed install and install it using the deb. I wrote an article about it on my blog for future reference...
https://computerobz.wordpress.com/2016/12/15/ttf-mscorefonts-installer-fails-to-installupgrade/

Basically:

1.) Launch a terminal and remove the failed install:

sudo apt-get remove --purge ttf-mscorefonts-installer

2.) Get the package and install it using the following three commands:

cd ~/Downloads/

sudo wget http://mirrors.linux.iu.edu/linux/debian/pool/contrib/m/msttcorefonts/ttf-mscorefonts-installer_3.6_all.deb

sudo dpkg -i ttf-mscorefonts-installer_3.6_all.deb

Problem solved.