Radar SLAM is robust in challenging conditions, such as fog, dust, and smoke, but suffers from the sparsity and noisiness of radar sensing, including speckle noise and multipath effects. This study provides a performance-enhanced radar SLAM system by incorporating point uncertainty. The basic system is a radar-inertial odometry system that leverages velocity-aided radar points and high-frequency inertial measurements. We first propose to model the uncertainty of radar points in polar coordinates by considering the nature of radar sensing. Then, the proposed uncertainty model is integrated into the data association module and incorporated for back-end state estimation. Real-world experiments on both public and self-collected datasets validate the effectiveness of the proposed models and approaches. The findings highlight the potential of incorporating point uncertainty to improve the radar SLAM system. We make the code and collected dataset publicly available at https://github.com/HKUST-Aerial-Robotics/RIO.