Weakly supervised anomaly detection is a challenging task since frame-level labels are not given in the training phase. Previous studies generally employ neural networks to learn features and produce frame-level predictions and then use multiple instance learning (MIL)-based classification loss to ensure the interclass separability of the learned features; all operations simply take into account the current time information as input and ignore the historical observations. According to investigations, these solutions are universal but ignore two essential factors, i.e., the temporal cue and feature discrimination. The former introduces temporal context to enhance the current time feature, and the latter enforces the samples of different categories to be more separable in the feature space. In this article, we propose a method that consists of four modules to leverage the effect of these two ignored factors. The causal temporal relation (CTR) module captures local-range temporal dependencies among features to enhance features. The classifier (CL) projects enhanced features to the category space using the causal convolution and further expands the temporal modeling range. Two additional modules, namely, compactness (CP) and dispersion (DP) modules, are designed to learn the discriminative power of features, where the compactness module ensures the intraclass compactness of normal features, and the dispersion module enhances the interclass dispersion. Extensive experiments on three public benchmarks demonstrate the significance of causal temporal relations and feature discrimination for anomaly detection and the superiority of our proposed method.