Error detection (ED) in tabular data is crucial yet challenging due to diverse error types and the need for contextual understanding. Traditional ED methods often rely heavily on manual criteria and labels, making them labor-intensive. Large language models (LLM) can minimize human effort but struggle with errors requiring a comprehensive understanding of data context. In this paper, we propose ZeroED, a novel hybrid zero-shot error detection framework, which combines LLM reasoning ability with the manual label-based ED pipeline. ZeroED operates in four steps, i.e., feature representation, error labeling, training data construction, and detector training. Initially, to enhance error distinction, ZeroED generates rich data representations using error reason-aware binary features, pre-trained embeddings, and statistical features. Then, ZeroED employs LLM to label errors holistically through in-context learning, guided by a two-step reasoning process for detailed error detection guidelines. To reduce token costs, LLMs are applied only to representative data selected via clustering-based sampling. High-quality training data is constructed through in-cluster label propagation and LLM augmentation with verification. Finally, a classifier is trained to detect all errors. Extensive experiments on seven public datasets demonstrate that, ZeroED substantially outperforms state-of-the-art methods by a maximum 30% improvement in F1 score and up to 90% token cost reduction.