Nyquist plot disagreeing with the unity step response of the closed loop
Please double check the simulation/plots. That behavior seems way too fast ("noisy") for the dynamics of your system. I tried simulating the closed loop system in Octave and could notice that there is an unstable pole cancellation, but that does not lead to the "unstable" behavior in Octave.

I would say that is a problem in WolframAlpha and not really a control theory thing.  






s = tf('s')
l = 10(s+1)(s+2)/((s−3)(s−4))
pzmap(l/(1+l))
step(l/(1+l),40)