Non-Newtonian rheology can have a significant effect on mixing efficiency, which remains poorly understood. The effect of shear-thinning rheology in a Taylor-Couette reactor is studied using a combination of particle image velocimetry and flow visualization. Shear-thinning is found to alter the critical Reynolds numbers for the formation of Taylor vortices and the higher-order wavy instability, and is associated with an increase in the axial wavelength. Strong shear-thinning and weak viscoelasticity can also lead to sudden transitions in wavelength as the Reynolds number is varied. Finally, it is shown that shear-thinning causes an increase in the mixing time within vortices, due to a reduction in their circulation, but enhances the axial dispersion of fluid in the reactor.