Difference Amplifier - Signal Attenuation
You can null out the CMRR error, once. 

But if your high-voltage line or whatever you are monitoring, is bouncing around, the AC_CMRR becomes important.

So you should quantify the trash/hum/ripple/spikes on the signal you are monitoring, versus frequency. Then compare that to the CMRR VERSUS FREQUENCY curve of your circuit.