I have exactly the same problem: The tactics trainer hung up after my first move. I thought it could have been a bug or a delay on my computer, but your message reassured me it is a programming bug.
It is a little frustrating because we lose points when we have the first move wrong, but we don't get points when it is right because it does not progress... More interesting I did twice the same problem and got different answers for the first move:
First time, the move was right, the trainer stopped, I left, then came back using the undo arrow, re-played my move... and it said it was wrong! 
Hi All-
Tactics trainer seems to hang after the first move. fwiw