Electrocardiograms (ECGs) are crucial for cardiac diagnostics, but current audit practices often employ random selection, resulting in inefficiency and overlooking valuable analytical insights. To optimize resource allocation and enhance audit outcomes, a targeted approach is needed, prioritizing ECGs with high diagnostic ambiguity or clinical relevance. This study introduces an automated method for identifying such high-utility ECGs using graph-based features derived from visibility graphs and time series features. By transforming ECGs into graph representations and using their time series properties, we enhance the discrimination of four key conditions: right bundle branch block (RBBB), left bundle branch block (LBBB), sinus tachycardia (ST), and sinus bradycardia (SB). These features capture complex, non-linear relationships in ECG data, enabling more nuanced clustering than conventional methods. Our approach not only streamlines medical audits by targeting the most informative ECGs but also demonstrates the untapped potential of graph theory combined with time series in cardiac diagnostics. By reducing reliance on random sampling, this method can improve audit efficiency by over four times, reducing costs, and ultimately supporting better clinical decision-making.