Automated retinal vessel segmentation is crucial to the early diagnosis and treatment of ophthalmological diseases. Many deep-learning-based methods have shown exceptional success in this task. However, current approaches are still inadequate in challenging vessels (e.g., thin vessels) and rarely focus on the connectivity of vessel segmentation. We propose using an error discrimination network (D) to distinguish whether the vessel pixel predictions of the segmentation network (S) are correct, and S is trained to obtain fewer error predictions of D. Our method is similar to, but not the same as, the generative adversarial network. Three types of vessel samples and corresponding error masks are used to train D, as follows: (1) vessel ground truth; (2) vessel segmented by S; (3) artificial thin vessel error samples that further improve the sensitivity of D to wrong small vessels. As an auxiliary loss function of S, D strengthens the supervision of difficult vessels. Optionally, we can use the errors predicted by D to correct the segmentation result of S. Compared with state-of-the-art methods, our method achieves the highest scores in sensitivity (86.19%, 86.26%, and 86.53%) and G-Mean (91.94%, 91.30%, and 92.76%) on three public datasets, namely, STARE, DRIVE, and HRF. Our method also maintains a competitive level in other metrics. On the STARE dataset, the F1-score and area under the receiver operating characteristic curve (AUC) of our method rank second and first, respectively, reaching 84.51% and 98.97%. The top scores of the three topology-relevant metrics (Conn, Inf, and Cor) demonstrate that the vessels extracted by our method have excellent connectivity. We also validate the effectiveness of error discrimination supervision and artificial error sample training through ablation experiments. The proposed method provides an accurate and robust solution for difficult vessel segmentation.