In this paper we show that radial distortion of images invalidates the geometric constraint on which self-calibration of a rotating camera is based - that 3D lines drawn between matched features all intersect at the rotation center. We develop a geometric picture showing how radial distortion violates this constraint and discuss the implications for self-calibration of a rotating camera. In particular, we show that the behavior of self-calibration is markedly different for pincushion and barreling distortion, the latter causing self-calibration to be unreliable or to fail completely. A method is presented for automatically estimating the radial distortion over a sequence of images, when both distortion and camera internal parameters vary. We discuss when such an approach will work and whether accurate automatic calibration of a rotating camera is possible.