While distant supervision has been extensively explored and exploited in NLP tasks like named entity recognition, a major obstacle stems from the inevitable noisy distant labels tagged unsupervisedly. A few past works approach this problem by adopting a self-training framework with a sample-selection mechanism. In this work, we innovatively identify two types of biases that were omitted by prior work, and these biases lead to inferior performance of the distant-supervised NER setup. First, we characterize the noise concealed in the distant labels as highly structural rather than fully randomized. Second, the self-training framework would ubiquitously introduce an inherent bias that causes erroneous behavior in both sample selection and eventually prediction.