Deep learning has made significant strides in automated brain tumor segmentation from magnetic resonance imaging (MRI) scans in recent years. However, the reliability of these tools is hampered by the presence of poor-quality segmentation outliers, particularly in out-of-distribution samples, making their implementation in clinical practice difficult. Therefore, there is a need for quality control (QC) to screen the quality of the segmentation results. Although numerous automatic QC methods have been developed for segmentation quality screening, most were designed for cardiac MRI segmentation, which involves a single modality and a single tissue type. Furthermore, most prior works only provided subject-level predictions of segmentation quality and did not identify erroneous parts segmentation that may require refinement. To address these limitations, we proposed a novel multi-task deep learning architecture, termed QCResUNet, which produces subject-level segmentation-quality measures as well as voxel-level segmentation error maps for each available tissue class. To validate the effectiveness of the proposed method, we conducted experiments on assessing its performance on evaluating the quality of two distinct segmentation tasks. First, we aimed to assess the quality of brain tumor segmentation results. For this task, we performed experiments on one internal and two external datasets. Second, we aimed to evaluate the segmentation quality of cardiac Magnetic Resonance Imaging (MRI) data from the Automated Cardiac Diagnosis Challenge. The proposed method achieved high performance in predicting subject-level segmentation-quality metrics and accurately identifying segmentation errors on a voxel basis. This has the potential to be used to guide human-in-the-loop feedback to improve segmentations in clinical settings.