The best thing to do in this situations is to just reload the site, a quick F5 press helps but yes the board breakes sometimes when you try illegal moves.
I also had this error after picking up a piece and then the opponent played his move before I clicked again to release the piece, it got stuck on the cursor.
I tried to premove Kf7, however it got stuck in this screen:
Note that the mouse is outside the screenshot here. I could not move the king.
In the developer tools, I see:
dojochess.v2015041401.js:14
exception in animation handler for: onEnd
d.extend._fire
TypeError: Cannot read property 'callback' of undefined
multiple times. After my time ran out, I could move again.