[_flux]

What does it do with a single probe, though? You need two to actually probe anything, right?

So I'm wondering how is the second probe problem dealth with. I've considered something similar but with small weight attached to a pogo pin, so the CNC arm could then just move it around, which would not be very easy to get completely reliable as there may be components on the board.

[s_m_t]

Your common oscilloscope is common ground referenced. You attach to your test circuits ground with the typically black alligator clips coming off the probe and then read voltage at a point with the test lead. A decent differential probe like you might be thinking of usually costs about as much as a decent hobbyist oscilloscope.

[_flux]

Ah well that does simplify things significantly, I suppose it's probably still somewhat useful.

But I'd expect a big part of the nets are not connected to the ground? I mean in my hobby designs a majority of them is, but let's say if you generously use decoupling capacitors, then that might not be the case?

[Majromax]

Decoupling capacitors don't remove the ground reference, they just allow high-frequency signals a faster path to ground.

Typically, you need dedicated circuitry (and usually inductive coupling) to provide full isolation, but if the circuit is using this layout then you can still choose to ground the normally-isolated side for probing.

[SAI_Peregrinus]

"the ground" ≠ "ground". It's unfortunate naming IMO, but "ground" is just the 0V reference point. A normal oscilloscope's ground probes are mains Earth referenced, that is they're connected to the "ground" pin in the outlet which in turn connects to one or more conductive rods buried in the Earth. Decoupling capacitors don't negate the ground reference, since they're connected between a power rail & circuit ground. So the power rail's voltage is still referenced to ground.

A truly "floating" circuit would be something battery powered, or galvanically isolated from mains Earth (e.g. by an isolation transformer).