Conflicting sensor measurements pose a huge problem for the environment representation of an autonomous robot. Therefore, in this paper, we address the self-assessment of an evidential grid map in which data from conflicting LiDAR sensor measurements are fused, followed by methods for robust motion planning under these circumstances. First, conflicting measurements aggregated in Subjective-Logic-based evidential grid maps are classified. Then, a self-assessment framework evaluates these conflicts and estimates their severity for the overall system by calculating a degradation score. This enables the detection of calibration errors and insufficient sensor setups. In contrast to other motion planning approaches, the information gained from the evidential grid maps is further used inside our proposed path-planning algorithm. Here, the impact of conflicting measurements on the current motion plan is evaluated, and a robust and curious path-planning strategy is derived to plan paths under the influence of conflicting data. This ensures that the system integrity is maintained in severely degraded environment representations which can prevent the unnecessary abortion of planning tasks.