First of all thank you on your replies, and helpful input!
Have you measured the voltage across the R with a meter when connected to the Arduino?
No I have not! But I have tried to measure resistance between arduino A0 and ground it is 150ohm, and between A1 and GND is about 700ohms (when arduino is not connected to power). I will update on this!
I would first make a simple resistor divider to produce some voltage between 1 and 4 volts to make sure the analog input and program is working correctly. Then I would put the transmitter back into the circuit. My gut tells me you do have a ground reference issue. The which wall outlet they are plugged into means very little. I would get a 9VDC power supply for the arduino and then tie the grounds for the 9VDC and 24VDC together.
A 4-20mA transmitter is a simple device but stumps many people. The big picture circuit is 24VDC to the instrument, out of the instrument comes some semi-random voltage to produce the current necessary to drive the line loss resistance and the 250ohm precision resistor at the receiver plus the line loss resistance back to the device. The A/D needs to be connected across the 250 ohm resistor which means one side is voltage signal and the other is ground. If you have two difference grounds, then you will need to develop a loop isolator to place between the device signal and the arduino, so you can measure across the resistor.
Noted! I have tested the analog input with potentiometer, and with 3.3V psu - it worked OK. I will perform this test again, but I have to wait till Monday to get it :(.
So your advice is to use 9V battery to power arduino and to connect the grounds with the 24V psu. Can you make a picture or a scheme of it?
I have drawn the scheme to make it more clear.