Is there any biblical justification for referring to God as Mother? On one occasion, I heard someone prayer, "To God, our Father and Mother." In The Shack, the Trinity is represented as three persons, where God the Father is a woman.

Is there any biblical justification for referring to God as Mother?  

Are there any denominations or movements which do call the first person of the trinity 'Mother'?
There is a significant distinction between calling God "mother" and the Bible identifying aspects of motherhood (and fatherhood) as reflecting the glory and character of God.

Both men and women reflect the glory and character of God in different ways, as men and women, fathers and mothers, teachers, judges, etc.

However, God is spirit (John 4:23) and not physical.  In the beginning, God created the physical universe, including genders.  Yet, He Himself was not biological, but is and was outside of creation.

When He entered into creation, He did enter into it as a Man.  In the Lord's prayer, God the Son instructs us to refer to God the Father as "Our Father" (Matthew 6:9-13).  Nowhere in Scripture are we instructed to refer to God as mother.

The example of Paul is of note as well.  He himself indicated that he cared for the Thessalonians like a mother cares for her children:


  But we were gentle[c] among you, like a nursing mother taking care of
  her own children.  1 Thessalonians 2:7 ESV


But no one used that as a basis for calling Paul "Mom".

This in no way disparages women, and both men and women reflect the glory of God.  Yet, God has chosen to reveal Himself in the masculine sense.  If we are devoted believers, we recognize that He is the One who has the right to define how we should refer to Him--not us.