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The rapid evolution of computational and data-driven materials engineering has introduced closed-loop systems that integrate simulation, machine learning, and experimental validation to accelerate materials discovery. However, these infrastructures raise critical questions about accountability, encompassing liability distribution across computational workflows, ownership of validation processes, attribution of errors in predictive models, and broader regulatory implications for deployment in high-stakes applications. This review synthesizes recent advancements in uncertainty quantification, error evaluation, and automated frameworks within computational materials ecosystems, highlighting how they underpin accountability mechanisms. We examine liability in multi-stage pipelines where uncertainties propagate from atomic simulations to macroscopic predictions, as seen in neural network potentials and Bayesian active learning approaches. Validation ownership is dissected through ensemble methods and adversarial techniques that assign responsibility for model reliability. Error attribution is explored via metrics and information-theoretic tools that trace discrepancies back to data sources or algorithmic biases. Regulatory considerations are framed around numerical quality controls and convergence protocols essential for certifying computational outputs in sectors like additive manufacturing and thermoelectric materials. By integrating cross-study insights, we propose an original interpretive structure for accountability infrastructures, emphasizing closed-loop feedback as a means to mitigate risks. This synthesis underscores the need for standardized protocols to ensure trustworthy integration of AI-driven tools in materials engineering, paving the way for ethical and reliable innovation.