I, too, ran into this problem. I found a way to move the annotation without moving the leader line anchor point. I have not found a way to move the anchor point, however. In your map, select the Edit tab, then click on Modify. The Modify Features window pops up, and you can select a tool called Annotation. If you use this tool to select and move your annotation, the anchor point should stay with the feature. At least it did on mine. There still seem to be a few bugs with my annotation, though....