Deep learning has achieved state-of-the-art performance in automated brain tumor segmentation from magnetic resonance imaging (MRI) scans. However, the unexpected occurrence of poor-quality outliers, especially in out-of-distribution samples, hinders their translation into patient-centered clinical practice. Therefore, it is important to develop automated tools for large-scale segmentation quality control (QC). However, most existing QC methods targeted cardiac MRI segmentation which involves a single modality and a single tissue type. Importantly, these methods only provide a subject-level segmentation-quality prediction, which cannot inform clinicians where the segmentation needs to be refined. To address this gap, we proposed a novel network architecture called QCResUNet that simultaneously produces segmentation-quality measures as well as voxel-level segmentation error maps for brain tumor segmentation QC. To train the proposed model, we created a wide variety of segmentation-quality results by using i) models that have been trained for a varying number of epochs with different modalities; and ii) a newly devised segmentation-generation method called SegGen. The proposed method was validated on a large public brain tumor dataset with segmentations generated by different methods, achieving high performance on the prediction of segmentation-quality metric as well as voxel-wise localization of segmentation errors. The implementation will be publicly available at https://github.com/peijie-chiu/QC-ResUNet.