Automatic sound classification has a wide range of applications in machine listening, enabling context-aware sound processing and understanding. This paper explores methodologies for automatically classifying heterogeneous sounds characterized by high intra-class variability. Our study evaluates the classification task using the Broad Sound Taxonomy, a two-level taxonomy comprising 28 classes designed to cover a heterogeneous range of sounds with semantic distinctions tailored for practical user applications. We construct a dataset through manual annotation to ensure accuracy, diverse representation within each class and relevance in real-world scenarios. We compare a variety of both traditional and modern machine learning approaches to establish a baseline for the task of heterogeneous sound classification. We investigate the role of input features, specifically examining how acoustically derived sound representations compare to embeddings extracted with pre-trained deep neural networks that capture both acoustic and semantic information about sounds. Experimental results illustrate that audio embeddings encoding acoustic and semantic information achieve higher accuracy in the classification task. After careful analysis of classification errors, we identify some underlying reasons for failure and propose actions to mitigate them. The paper highlights the need for deeper exploration of all stages of classification, understanding the data and adopting methodologies capable of effectively handling data complexity and generalizing in real-world sound environments.