Just discovered a major bug.
If you move a character as soon as his turn starts (a split second after the yellow ring appears, or already holding a direction when the turn starts), the Done button will do nothing. Clicking another character doesn't work either. Undo still works, and attacking ends the turn as usual, but the game is stuck if there are no targets in range. Fortunately, pressing X seems to fix this.
Also, confirming the above post, I had Luca go into negative PsP after using Transfer 2 with four other characters around her. She had 23 before using it, transferred 44 total, 11 to each character, and ended with -21.