If I'm reading the rules correctly (and at 1:30 in the morning that's a big 'ol IF), I do believe that it's possible to have a violation during a dead ball.

6-1-2-a The ball becomes live when: On a jump ball, the tossed ball leaves the referee's hand(s).

6-3-2 When the referee is ready and until the ball is tossed, nonjumpers shall not...
a. Move onto the center restraining circle.
b. Change positions around the center restraining circle.

9-6 A player shall not violate any provision of the jump ball (6-3)....PENALTY: The ball is dead when the violation occurs and is awarded to the opponents for a throw-in from the deignated out-of-bounds spot nearest the violation.

In that short period of time between the referee is ready to toss and the moment it actually leaves his hand, you could have a violation during a dead ball.

Just as an example, the referee is ready to toss it, but has not yet, when A3 steps up onto the circle. Ball is still dead, but you've got a jump ball violation. Am I reading this right?

Are there any other situations like this where you can have a violation during a dead ball?

Yes. Swinging elbows after a made shot and before the ball is at the disposal of the thrower.