Glitchy! Moving Object Distorts Beyond Recognition

[MontyDraws]

I am having a terrible time with the newest version of illustrator. Here I am simply clicking on a grouped object to move it. When I click it turns into a completely different shape. 

 

 

  

[tromboniator]

Does it make a difference whether you view it in GPU or CPU mode (View menu or cmd/ctrl + E)? Some sort of effect applied to the group?

Peter