Water quality is foundational to environmental sustainability, ecosystem resilience, and public health. Deep learning models, particularly Long Short-Term Memory (LSTM) networks, offer transformative potential for large-scale water quality prediction and scientific insights generation. However, their widespread adoption in high-stakes decision-making, such as pollution mitigation and equitable resource allocation, is prevented by unresolved trustworthiness challenges including fairness, uncertainty, interpretability, robustness, generalizability, and reproducibility. In this work, we present the first comprehensive evaluation of trustworthiness in a continental-scale multi-task LSTM model predicting 20 water quality variables (encompassing physical/chemical processes, geochemical weathering, and nutrient cycling) across 482 U.S. basins. Our investigation uncovers systematic patterns of model performance disparities linked to basin characteristics, the inherent complexity of biogeochemical processes, and variable predictability, emphasizing critical performance fairness concerns. We further propose methodological frameworks for quantitatively evaluating critical aspects of trustworthiness, including uncertainty, interpretability, and robustness, identifying key limitations that could challenge reliable real-world deployment. This work serves as a timely call to action for advancing trustworthy data-driven methods for water resources management and provides a pathway to offering critical insights for researchers, decision-makers, and practitioners seeking to leverage artificial intelligence (AI) responsibly in environmental management.