Vox Veritatis has some thoughts on the problems with the English expression "Mother of God." (link to comments) Of course, there is an orthodox sense to the term (the orthodox sense is that Mary was the mother of Jesus, who is God incarnate), but the resultant expression is awkward at best.
The only argument for the expression is that Jesus is God, Jesus is the Son of Mary, therefore Mary is the mother of God. But Jesus is also the Son of David. Any takers for calling David "the Father of God" or the "Ancestor of God"?
Unsurprisingly, there are few takers for this kind of expression. The reason why is intuitive. It just sounds inappropriate. It similarly sounds inappropriate to call Mary the Mother of God (to those of us who have not become desensitized to the expression), since she did not provide Jesus' divinity: only Jesus' humanity was taken from Mary.