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Machine learning molecular dynamics has become a cornerstone for exploring solid-state electrolytes in next-generation batteries. Researchers rely on these potentials to predict ionic conductivity, lithium diffusion, and phase behavior at speeds far beyond traditional density functional theory while maintaining near-DFT accuracy. Yet a critical gap remains: most ML potentials are trained exclusively on static, zero-kelvin structures and energies. When deployed in finite-temperature simulations between 300 K and 1000 K—the actual operating regime of solid-state electrolytes—hidden instabilities emerge that standard benchmarks never detect. This failure-mode analysis identifies five specific instabilities that compromise the reliability of ML-driven molecular dynamics for solid-state electrolytes. Energy drift in long NVT or NVE runs violates conservation laws and produces artificial heating or cooling. Unphysical lithium diffusion pathways appear because transition states and saddle-point configurations are absent from training data, leading to either barrierless motion or spurious trapping. Force discontinuities arise from non-smooth descriptor cutoffs and become amplified by thermal motion. Phonon softening is mispredicted, distorting the vibrational precursors to superionic transitions. Finally, the superionic transition itself is either shifted by more than 100 K, entirely absent, or incorrectly sharp or gradual. These instabilities are invisible in conventional zero-kelvin tests such as energy mean-absolute error or force root-mean-square error on equilibrium structures. They only surface during extended nanosecond-scale simulations at operating temperatures. The present work systematically dissects why each failure mode occurs, provides clear detection signatures observable in any ML molecular-dynamics workflow, and outlines practical mitigation strategies grounded in the literature. By treating finite-temperature stability as a core validation requirement rather than an afterthought, the field can move from promising prototypes to trustworthy tools for solid-state electrolyte design. The analysis draws on recent advances in machine-learning interatomic potentials while highlighting the urgent need for temperature-aware training and testing protocols.