I'm going to tell my friend that his wife's picture was inappropriate and potentially hurtful
That could be bad. Why do you feel his wife's picture was inappropriate and harmful?
I think it's wrong to post her face online for anyone to see
You shouldn't police what your friend posts online. A picture with her face in it isn't appropriate and you should lay off.
I'm going to send it to upper management and make it a political issue.
By doing that you'll be causing issues for your friend's wife. When your friend finds out that you reported his wife they will be very upset and may even end the friendship. Try settling this issue personally between you three before escalating the issue.