(1) For a pure component, the critical pressure always exceeds the vapor pressure at any other temperature.
(2) For a multicomponent mixture, the vapor pressure at the dew point temperature may exceed the "true" critical pressure. As noted by 25362, the cricondenbar is the point at which the saturation pressure is highest. The best way to see this is by making a "phase envelop" calculation. This is basically a P-T curve showing the entire locus of the equilibrium curve - saturated liquid and saturated vapor all the way to the critical point.
(3) For multicomponent systems, the thermodynamic option (equation of state) chosen can have a huge impact on the resulting calculation and one must use a great deal of experience and insight to make the proper choice. Therefore, I heartily endorse Morten's cautionary notes.