In machine learning, classification tasks serve as the cornerstone of a wide range of real-world applications. Reliable, trustworthy classification is particularly intricate in biomedical settings, where the ground truth is often inherently uncertain and relies on high degrees of human expertise for labeling. Traditional metrics such as precision and recall, while valuable, are insufficient for capturing the nuances of these ambiguous scenarios. Here, we introduce the concept of aberrant predictions, emphasizing that the nature of classification errors is as critical as their frequency. We propose a novel, efficient training methodology aimed at both reducing the misclassification rate and discerning aberrant predictions. Our framework demonstrates a substantial improvement in model performance, achieving a 20\% increase in precision. We apply this methodology to the less-explored domain of veterinary radiology, where the stakes are high but have not been as extensively studied compared to human medicine. By focusing on the identification and mitigation of aberrant predictions, we enhance the utility and trustworthiness of machine learning classifiers in high-stakes, real-world scenarios, including new applications in the veterinary world.