Besides overloads, shorts,age and heat from fellow breakers, What else will cause a breaker to trip?

Edward

Heat from a loose connection to Bus or Load.

Vibration

I've seen bad contacts on an a/c contactor heat up breakers to the point of tripping.

At one time, there was a solid state trip unit on a GE breaker that would trip when exposed to certain EMI. With some sheilding introduced by GE, it was rectified.