A complete description of the bifurcation scenario of a uniform flow past a rotating circular cylinder has been recently provided by [1]. Linear stability theory is used to depict neutral curves and analyse the arising unstable global modes. Special emphasis is paid to the identification of bifurcations with codimension higher than one. Three codimension-two bifurcation points are detected, namely a Takens-Bogdanov, a cusp and generalised Hopf, which are closely related to qualitative changes in orbit dynamics. The occurence of the cusp and Takens-Bogdanov bifurcations for very close parameters (corresponding to an imperfect codimension-3 bifurcation) is shown to be responsible for the emergence of multiple steady states. Direct numerical simulations confirmed the presence of homoclinic and heteroclinic orbits which are classical in the presence of Takens-Bogdanov bifurcations. Finally, a weakly nonlinear analysis is accomplished in the neighborhood of the Generalised Hopf bifurcation to determine the fold of two limit cycles of opposing stability in the vicinity the subcritical Hopf bifurcation curve.