If an animation only has a Frame 0, any chosen part can be rotated and moved freely with the mouse. Once another frame is added, that can no longer be done, and parts can only be moved using the Rotation and Position inputs below Duration.

I tested this with a basic model just incase it was because of the one I was already working on, but the issue persisted.

Downgrading to 0.6.1 solved the issue, but it was present in 0.6.2 and 0.6.3

I'm not quite sure how to help, but I'd thought I'd report this Bug