Visual odometry (VO) is a fundamental component in robotics and augmented reality. RGB-D direct VO benefits from metric depth measurements, but it can degrade in challenging environments, where dynamic objects, occlusions, illumination changes, and unreliable depth violate the short-horizon photometric and depth-geometric consistency assumptions used by direct alignment. Existing approaches mitigate these issues through semantic filtering, explicit occlusion reasoning, illumination adaptation, or hand-crafted geometric criteria, but often rely on external modules or fixed assumptions tailored to individual failure modes, limiting their flexibility and ability to handle diverse challenges in a unified manner. In this work, we propose Con-DSO, a consistency-aware RGB-D direct sparse odometry framework that predicts dense photometric and depth-geometric consistency uncertainty from temporally adjacent RGB-D frame pairs. The consistency network is trained using flow-guided photometric errors and projective depth-consistency errors, allowing consistency violations to be represented as pixel-level uncertainty. These pairwise uncertainty predictions are converted into a host-side quality prior for keyframe-based tracking. The prior is then applied to VO through quality-aware support-pixel selection and decoupled photometric-geometric weighting during pose estimation, enabling continuous attenuation of unreliable observations rather than hard rejection or threshold-based gating. Experiments on five public RGB-D benchmarks show substantial gains over direct RGB-D VO baselines, with over 20\% absolute trajectory error reduction on ICL-NUIM and 50\%--80\% reductions on RGB-D Scenes V2, TUM/Bonn Dynamic, and OpenLORIS sequences.