Using a cap to predict the presence of a pulse via voltmeter
As shown it's pretty dubious. You'll get a big pulse the first time the diode conducts and not much afterwards after some pulses in that direction, and then reverse pulses due to the diode capacitance, which may be larger than the forward ones.  

If you just put an RC (eg. 1M/1uF) in front of the meter on DC volts you should read the voltage of 5mV average without any more parts. 

You can model the meter by something like 10M resistor across the leads, followed by a low pass filter like 1M/0.1uF. But I don't think I'd feel comfortable feeding 250V pulses directly into the meter on the 200mV range.