Is the Nyquist plot a plot of Re(G(s)) v.s. Im(G(s) or Re(G(jω)) v.s. Im(G(jω))
From a practical point of view the Nyquist plot is the mapping of the imaginary axis from \$-j\infty\$ to \$j\infty\$ through the function 1 + G(s).

From an academic point of view it is the mapping of the Nyquist contour through 1+G(s). 

The Nyquist contour is again the imaginary axis from \$-j\infty\$ to \$j\infty\$ and then an arc that starts at \$0+j\omega\$ and goes clockwise to \$0-j\omega\$ with \$\omega\$ approaching infinity. The idea is to get a contour that encompasses the whole right half plane. Then Cauchy's principle of argument can be used to determine the difference (!) between the number of zeros and poles in the enclosed region.

If G(s) has low-pass characteristic then points at infinity will map into 1 since G(s) approaches zero. All practical systems have low-pass characteristic so the semicircle can be omitted.