With a typical 3 pin regulator and a series resistance at the input, the capacitor at the regulator input is essential, but otherwise the regulator may oscillate.
The size of the capacitor depends on the duration of the negative peak (blocked by the diode), but a very big high ESR capacitor may cause stability problems.
With 22-27 V zener, it will dissipate a small amount of current operation, thus upgrading the resistor and zener rating should solve this problem. The resistor+zener acts as a shunt regulator, further improving the noise performance.
If the output side of the regulator has a lot of capacitance, suddenly removing the input voltage (e.g. removing the battery), there will be a reverse polarity across the regulator, which many models do not like. For battery operated systems, put a reverse polarized diode between input and output.