An analytical and numerical study of the ideal magnetohydrodynamic (MHD) spectrum of waves and instabilities of a cylindrical plasma column with flows is presented. Our analytical results are relevant for thermally stratified, rotating, magnetized cylindrical equilibria. The presence of azimuthal flow makes the general analysis of the MHD spectrum difficult, except in cases where the continuous parts of the spectrum are absent. In the presence of Doppler shifted Alfvén and slow continua, a local analysis at resonant surfaces or internal extrema can provide a simple and reliable way to access information on MHD spectroscopy. In this paper, local cluster conditions, which govern the occurrence of sequences of discrete global modes, have been generalized for rotating equilibria. The generalized Suydam criterion for instability is revisited. A numerical study confirms our analytical results and clearly demonstrates how the local criteria govern the existence of the accumulating eigenmodes.