Quality control of structures segmentation in volumetric medical images is important for identifying segmentation errors in clinical practice and for facilitating model development. This paper introduces SegQC, a novel framework for segmentation quality estimation and segmentation error detection. SegQC computes an estimate measure of the quality of a segmentation in volumetric scans and in their individual slices and identifies possible segmentation error regions within a slice. The key components include: 1. SegQC-Net, a deep network that inputs a scan and its segmentation mask and outputs segmentation error probabilities for each voxel in the scan; 2. three new segmentation quality metrics, two overlap metrics and a structure size metric, computed from the segmentation error probabilities; 3. a new method for detecting possible segmentation errors in scan slices computed from the segmentation error probabilities. We introduce a new evaluation scheme to measure segmentation error discrepancies based on an expert radiologist corrections of automatically produced segmentations that yields smaller observer variability and is closer to actual segmentation errors. We demonstrate SegQC on three fetal structures in 198 fetal MRI scans: fetal brain, fetal body and the placenta. To assess the benefits of SegQC, we compare it to the unsupervised Test Time Augmentation (TTA)-based quality estimation. Our studies indicate that SegQC outperforms TTA-based quality estimation in terms of Pearson correlation and MAE for fetal body and fetal brain structures segmentation. Our segmentation error detection method achieved recall and precision rates of 0.77 and 0.48 for fetal body, and 0.74 and 0.55 for fetal brain segmentation error detection respectively. SegQC enhances segmentation metrics estimation for whole scans and individual slices, as well as provides error regions detection.