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Programming is an essential skill in computer science and in a wide range of engineering-related disciplines. However, occurring errors, often referred to as “bugs” in code, can indeed be challenging to identify and rectify, both for students who are learning to program and for experienced professionals. These errors can lead to unexpected behaviors in programming. Understanding, finding, and effectively dealing with errors is an integral part of programming learning as well as software development. To classify the errors, we propose a multi-label error classification of source code for dealing with programming data by using the ML-KNN classifier with CodeT5 embeddings. In addition, several deep neural network (DNN) models, including GRU, LSTM, BiLSTM, and BiLSTM-A (attention mechanism) are also employed as baseline models to classify the errors. We trained all the models by using a large-scale dataset (original error labels) as well as modified datasets (summarized error labels) of the source code. The average classification accuracy of the proposed model is 95.91% and 84.77% for the original and summarized error-labeled datasets, respectively. The exact match accuracy is 22.57% and 27.22% respectively for the original and summarized error-labeled datasets. The comprehensive experimental results of the proposed approach are promising for multi-label error classification over the baseline models. Moreover, the findings derived from the proposed approach and data-driven analytical results hold significant promise for error classification, programming education, and related research endeavors.