Seems like your mV source has an output impedance of 10 ohm, it would be a reasonable value in my opinion. Unfortunately
you're driving a huge current of 120 µA into the thermocouple, which is inappropriate for any thermocouple type, I think.
Small thermcouples can have up to 50 or 100 ohm resistance, so you get a temperature error of up to 200 degree C.
You may want to use at least 10 M resistors for the open input detection circuit.
Regarding ground potential differences: They are expectable, if a DC current is flowing through the ground net. Because you
didn't tell design details, there can't be said much more. As a special problem, has you're mV source an isolated supply? If not,
you should be aware that part of the supply current is flowing through your measurement ground.