Electronic – The resistance between the 1.2V rail and GND is 40 Ohms, is it safe

In general, trying to push final regulated power any distance is not a good idea. In your case it clearly won't work. Yes, the return path adds to the total resistance since it is in series with the load. It is strange that you have connectors in the positive supply but not in the ground. If this is a fixed installation, then why not solder wires from one end to the other?

A better way to deal with the need for distributed regulated power, especially at low voltage and high currents as you have, is to distribute a higher roughly regulated voltage and make the final tightly regulated voltage locally. This does two useful things:

1. The drop in distributing the higher voltage won't matter since is will be regulated anyway to the final voltage. You do have to make sure the voltage at the other is at least the minimum required for that regulator to work correctly, but that headroom is usually easy to build in.

2. In the case of local regulators being switchers, the higher voltage will have less current, which means it will also have less voltage drop accross the distance, with less power wasted and heat that must be dealt with.

So where does your 1.2V supply come from? You probably have some higher voltage with a buck converter somewhere. Send that higher voltage over the distance and put a buck regulator right at the DSP. Note that this relaxes the requirements on the 1.2V supply on the main board. Two smaller buck regulators will still be more expensive than one larger one, but allowing both to be smaller will help somewhat. It also distributes the heat from any losses, which usually makes that easier to deal with.

Added in response to your comment:

If you really really can't put a local regulator by the load, then the next best thing is to have a sense line coming back. This line reports that actual voltage at the far end back to the regulator on the main board. This voltage is used as feedback so that the voltage at the far end is what is regulated. The voltage at the regulator then will automatically be higher as needed to overcome the voltage drop on the way to the load. The sense line doesn't experience these voltage drops since it has very little current flowing thru it. It is just a voltage feedback signal.

If the ground connection also can have significant voltage drop, then it gets more tricky. Sometimes you use two sense lines and treat them differentially at the power supply. Sometimes you assume the forward and backward voltage drops will be about equal and add a little bit of gain in the sense circuit. Sometimes you just set the output of the supply a little higher to compensate for the nominal total voltage drop and not try to actively regulate around it at all.

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.