In order to tackle the challenge of unfavorable weather conditions such as rain and snow, radar is being revisited as a parallel sensing modality to vision and lidar. Recent works have made tremendous progress in applying spinning radar to odometry and place recognition. However, these works have so far ignored the impact of motion distortion and Doppler effects on spinning-radar-based navigation, which may be significant in the self-driving car domain where speeds can be high. In this work, we demonstrate the effect of these distortions on radar odometry using the Oxford Radar RobotCar Dataset and metric localization using our own data-taking platform. We revisit a lightweight estimator that can recover the motion between a pair of radar scans while accounting for both effects. Our conclusion is that both motion distortion and the Doppler effect are significant in different aspects of spinning radar navigation, with the former more prominent than the latter. Code for this project can be found at: https://github.com/keenan-burnett/yeti_radar_odometry