Nucleus detection and classification (NDC) in histopathology analysis is a fundamental task that underpins a wide range of high-level pathology applications. However, existing methods heavily rely on labor-intensive nucleus-level annotations and struggle to fully exploit large-scale unlabeled data for learning discriminative nucleus representations. In this work, we propose MUSE (MUlti-scale denSE self-distillation), a novel self-supervised learning method tailored for NDC. At its core is NuLo (Nucleus-based Local self-distillation), a coordinate-guided mechanism that enables flexible local self-distillation based on predicted nucleus positions. By removing the need for strict spatial alignment between augmented views, NuLo allows critical cross-scale alignment, thus unlocking the capacity of models for fine-grained nucleus-level representation. To support MUSE, we design a simple yet effective encoder-decoder architecture and a large field-of-view semi-supervised fine-tuning strategy that together maximize the value of unlabeled pathology images. Extensive experiments on three widely used benchmarks demonstrate that MUSE effectively addresses the core challenges of histopathological NDC. The resulting models not only surpass state-of-the-art supervised baselines but also outperform generic pathology foundation models.