How serious is a broken rocker arm shaft?

it could be serious ,if it sticks with a valve open the piston can hit it and warp the valve or damage the piston.bent push rod or damaged lifter, if you have it repaired have a compression test run on the whole engine there should be no more than a 10% difference in the pressures. if there is a low compression on that cylinder there is some kind of damage,possibly unrelated to the rocker arm ,but serious.