Salient object detection (SOD) in panoramic video is still in the initial exploration stage. The indirect application of 2D video SOD method to the detection of salient objects in panoramic video has many unmet challenges, such as low detection accuracy, high model complexity, and poor generalization performance. To overcome these hurdles, we design an Inter-Layer Attention (ILA) module, an Inter-Layer weight (ILW) module, and a Bi-Modal Attention (BMA) module. Based on these modules, we propose a Spatial-Temporal Dual-Mode Mixed Flow Network (STDMMF-Net) that exploits the spatial flow of panoramic video and the corresponding optical flow for SOD. First, the ILA module calculates the attention between adjacent level features of consecutive frames of panoramic video to improve the accuracy of extracting salient object features from the spatial flow. Then, the ILW module quantifies the salient object information contained in the features of each level to improve the fusion efficiency of the features of each level in the mixed flow. Finally, the BMA module improves the detection accuracy of STDMMF-Net. A large number of subjective and objective experimental results testify that the proposed method demonstrates better detection accuracy than the state-of-the-art (SOTA) methods. Moreover, the comprehensive performance of the proposed method is better in terms of memory required for model inference, testing time, complexity, and generalization performance.