I understand the basics behind the concept of common mode voltage and CMRR and friends, in the context of differential amplification.
What I don't understand is the determining if the whole concept of "common mode voltage" actually applies to a given circuit. That is, sometimes the signal being measured (i.e., the V+ and V-) doesn't have any particular relationship to the supply voltage. In that case, how can a common more voltage even be determined? The V+ and V- might be 1001V and 1000V or 1V and 0V - since voltage is relative I can't see how the amp would even know the difference.
For example, consider the case of a handheld multimeter - it's seems pretty clear that there the concept of common mode voltage wouldn't apply here. The voltmeter should perform identically in the 1001 V- and 1000 V+ case as the 1 V+ and 0 V- case (indeed, they aren't really distinguishable, are they)?
So if a dirty cheap voltmeter can simply avoid the whole question of staying inside the supply rails, and have a "perfect" CMRR, why is it such an issue for most components? I.e., components with very high CMRR are expensive, and require special designs, etc.