Old switch tripping breaker after a different one was replaced
If you have a switch that is tripping two breakers. Then chances are somewhere in your circuitry you have caused a phase to phase short. Re-examine the switch you replaced and see if you can find where you have crossed the phases. It wouldn't hurt to have a voltmeter with you so you can measure any wires where you are reading 240V between conductors. Or by turning your tripped breakers on and off you can see which conductors are crossing over.

Even if it's not at your switch, it's really just a matter of tracing out each tripped circuit and finding where they are intersecting. It's also very possible that the short is connected through a neutral.

Good luck

Also see Harpers comment on devices.