Human data annotation is critical in shaping the quality of machine learning (ML) and artificial intelligence (AI) systems. One significant challenge in this context is posed by annotation errors, as their effects can degrade the performance of ML models. This paper presents a predictive error model trained to detect potential errors in search relevance annotation tasks for three industry-scale ML applications (music streaming, video streaming, and mobile apps) and assesses its potential to enhance the quality and efficiency of the data annotation process. Drawing on real-world data from an extensive search relevance annotation program, we illustrate that errors can be predicted with moderate model performance (AUC=0.65-0.75) and that model performance generalizes well across applications (i.e., a global, task-agnostic model performs on par with task-specific models). We present model explainability analyses to identify which types of features are the main drivers of predictive performance. Additionally, we demonstrate the usefulness of the model in the context of auditing, where prioritizing tasks with high predicted error probabilities considerably increases the amount of corrected annotation errors (e.g., 40% efficiency gains for the music streaming application). These results underscore that automated error detection models can yield considerable improvements in the efficiency and quality of data annotation processes. Thus, our findings reveal critical insights into effective error management in the data annotation process, thereby contributing to the broader field of human-in-the-loop ML.