Latent world models are a promising approach for learning state representations and dynamics directly from high-dimensional observations, enabling robot control in hard-to-model settings. However, control performance ultimately depends on the latent representation encoding the required information for the task. In this work, we study latent-space safe control problems and show how partial observability can induce control failures when safety-relevant information is not preserved in the latent state. Specifically, we identify two world model failure modes: estimation gaps, where current observations do not reveal safety-critical quantities (e.g., temperature in a cooking task), and prediction gaps, where failures are observable once they occur but cannot be reliably anticipated from available observations. We introduce two diagnostics for these gaps: a mutual-information-based measure of safety observability and a rollout-based measure of future safety predictability. Finally, we present mitigation strategies for each failure mode: privileged multimodal supervision for estimation gaps and conformal risk calibration for prediction gaps. Across two hardware case studies -- using unimodal RGB world models and multimodal RGB+Tactile and RGB+Thermal variants -- we show that these mitigation strategies improve the safety of a Franka Research 3 manipulator on challenging cooking tasks under partial observability, albeit with increased conservativeness. More broadly, our work raises the question of when world model state representations are sufficient for reliable robot control