Tests to verify complete functionality of a PCB
Depends on how deep down the rabbit hole you want to go.

I'll list some tests that are done on pretty much every power supply I work on:


Load regulation:


Start at minimum load, or 5%-10% load and then step the load to 100% of your rated output and then back again. This can be done with an electronic load or some kind of mosfet + resistor circuit. Monitor output voltage on a scope. Take note of how far the voltage dips during 0->100, how far it surges during 100->0, and how long it takes to settle back to regulation. This is also a good way to estimate your phase margin if you don't have an analyzer.

Line regulation:


Measure your output voltage at nominal input, then at the lowest acceptable input and the highest acceptable input. Line regulation = (High-Low)/Nominal.

Ripple/Noise:


You already suggested this one, but it is a good thing to measure. Even if only to match with your maths.

Efficiency:


Power Out/Power In, easy peezy.

Short circuit/current limit:


What happens if you short circuit your supply? Does it have protections? Before doing a short, I'd lower your load resistance past 100% load and see how the supply reacts. Only do this if you put protections in place, I don't want to be responsible for hurting your supply.



For DC/DC converters, you can also test PSRR by injecting noise on top of your input voltage and seeing how much it is attenuated on the output. Requires a spectrum analyzer or a good scope.

There is much more out there, but like Andy said, it really depends on what you built, and what you deem acceptable. If you aren't making this for a customer or what have you, then it is all up to you.