Previous work on plant disease detection demonstrated that object detectors generally suffer from degraded training data, and annotations with noise may cause the training task to fail. Well-annotated datasets are therefore crucial to build a robust detector. However, a good label set generally requires much expert knowledge and meticulous work, which is expensive and time-consuming. This paper aims to learn robust feature representations with inaccurate bounding boxes, thereby reducing the model requirements for annotation quality. Specifically, we analyze the distribution of noisy annotations in the real world. A teacher-student learning paradigm is proposed to correct inaccurate bounding boxes. The teacher model is used to rectify the degraded bounding boxes, and the student model extracts more robust feature representations from the corrected bounding boxes. Furthermore, the method can be easily generalized to semi-supervised learning paradigms and auto-labeling techniques. Experimental results show that applying our method to the Faster-RCNN detector achieves a 26% performance improvement on the noisy dataset. Besides, our method achieves approximately 75% of the performance of a fully supervised object detector when 1% of the labels are available. Overall, this work provides a robust solution to real-world location noise. It alleviates the challenges posed by noisy data to precision agriculture, optimizes data labeling technology, and encourages practitioners to further investigate plant disease detection and intelligent agriculture at a lower cost. The code will be released at https://github.com/JiuqingDong/TS_OAMIL-for-Plant-disease-detection.