Point-wise supervision is widely adopted in computer vision tasks such as crowd counting and human pose estimation. In practice, the noise in point annotations may affect the performance and robustness of algorithm significantly. In this paper, we investigate the effect of annotation noise in point-wise supervision and propose a series of robust loss functions for different tasks. In particular, the point annotation noise includes spatial-shift noise, missing-point noise, and duplicate-point noise. The spatial-shift noise is the most common one, and exists in crowd counting, pose estimation, visual tracking, etc, while the missing-point and duplicate-point noises usually appear in dense annotations, such as crowd counting. In this paper, we first consider the shift noise by modeling the real locations as random variables and the annotated points as noisy observations. The probability density function of the intermediate representation (a smooth heat map generated from dot annotations) is derived and the negative log likelihood is used as the loss function to naturally model the shift uncertainty in the intermediate representation. The missing and duplicate noise are further modeled by an empirical way with the assumption that the noise appears at high density region with a high probability. We apply the method to crowd counting, human pose estimation and visual tracking, propose robust loss functions for those tasks, and achieve superior performance and robustness on widely used datasets.