Consider the following commands:

disk[z_] := Abs[z] <= 1
f[z_] := 1/z;
{ComplexRegionPlot[disk[z], {z, 3}],
 ComplexRegionPlot[disk[InverseFunction[f][z]], {z, 3}]}

Evaluation of these gives a few errors:

LessEqual::nord: Invalid comparison with ComplexInfinity attempted.
Power::infy: Infinite expression 1/0 encountered.
Power::infy: Infinite expression 1/0 encountered.
LessEqual::nord: Invalid comparison with ComplexInfinity attempted.

In the documentation (Applications -> Mapping Complex Regions) the authors applied Quiet to this last line:

{ComplexRegionPlot[disk[z], {z, 3}, PlotLabel -> z],
 Quiet@ComplexRegionPlot[disk[InverseFunction[f][z]], {z, 3}, 
   PlotLabel -> f[z]]}

Is there any problem with those errors one recieves without Quiet? How can I know when it is ok to quiet messages?