Have a look at the output of the supply as you plug and un-plug it.?
DC couple and trigger off of the output and you are looking for spikes and excursions during turn on and off.?
Repeat by connecting and disconnecting a load resistor if you have one while the unit stays powered on.? Again, you are looking for anything which indicates lack of stability and good regulation.
Hardest test I saw, a guy dragged a coarse file across the output studs of a (very hefty) power supply; he said if there were any instabilities or oscillations that would trigger them.
Then leave it powered on, AC couple and look for AC hum, switching-related spikes, etc., both with and without load, zoomed in to lower volts/div settings.
73, Don N2VGU?
Donald S Brant Jr