Electronic – Which components can be measured while soldered on a PCB board already

Here's a relatively simple solution, but not necessarily a cheap one (depending on your budget).

An oscilloscope is not likely to give you the accuracy you asked for because they typically use an 8-bit ADC, giving 0.2% in measurement uncertainty just from the sampling digitization.

Instead, consider simply using two benchtop multimeters, like Agilent 34401A's. I haven't looked at other models, but the 34401A can measure current at the accuracy you need (for example, 0.05% of reading + 0.005% of full-scale on the 100 mA range).

They can be triggered externally at 300 readings / second (for 5-1/2 digit resolution), so that gets you a sample window much shorter than your load switching cycle. If you hook the meters up to measure the input and output current, then trigger them simultaneously you'll be able to compare the results to determine the efficiency (assuming the input and output voltages are holding constant).

If the input and output voltages are also changing, you may need 4 multimeters to get all the information you need.

If you can synchronize your measurement to the moments when the load switches, you only need half as many multimeters, because you can first measure how the input current & voltage change in response to the load switch and then move the meters around and measure how the output responds to the switching event.

Because there is current flowing thru the ground wire between your PCB and the common ground point. The wire has a small resistance. The current time this resistance causes a offset voltage. For example, if there were 1 A flowing in the wire, then it would only need to have 23 mΩ resistance to exhibit the 23 mV offset.

Another more subtle possibility is that you have high frequencies in the system that are confusing the meter electronics. Above some frequency, probably somewhere in the 10s of kHz to 100s of kHz range, some meters without adequate filtering may start seeing AC as DC. Old purely mechanical meters are pretty much immune to this, but modern meters with active electronic front ends provide various ways for high frequency AC to be treated non-symmetrically and therefore to add a offset to the DC measurement. That all said, this is rather less likely than the much simpler explanation of a offset voltage accross the ground wire due its resistance times current thru it.