Spectroscopic single-molecule localization microscopy (sSMLM) generates super-resolution images of single molecules while simultaneously capturing the spectra of their fluorescence emissions. However, sSMLM splits photons from single-molecule emissions into a spatial channel and a spectral channel, reducing both channels' precisions. It is also challenging in transmission grating-based sSMLM to achieve a large field-of-view (FOV) and avoid overlap between the spatial and spectral channels. The challenge in FOV has further significance in single-molecule tracking applications. In this work, we analyzed the correlation between the spatial and spectral channels in sSMLM to improve its spatial precision, and we developed a split-mirror assembly to enlarge its FOV. We demonstrate the benefits of these improvements by tracking quantum dots. We also show that we can reduce particle-identification ambiguity by tagging each particle with its unique spectral characteristics.