In order to see some details on a Nyquist Diagram I have used the function NyquistPlot that comes with Mathematica v8 and v9.
NyquistPlot[ TransferFunctionModel[(30000*(s + 3)^2)/(s*(s + 0.5)^2*(s + 20)^2), s], Automatic, PlotPoints -> 1000, ImageSize -> Medium]
The first thing one can see is that there is a discontinuity (not in the actual diagram). Note that the dashed lines are departing from the wrong position of the branches.
I have tried to adjust the range of frequencies so as to see "more" of the diagram but to no avail.
One info: there are three crossings on the negative real axis (x-axis): -3.7, -56.5, -1074. I wonder whether there is a way to see them all.