Recent advancements in large language models (LLMs) have considerably advanced the capabilities of summarization systems. However, they continue to face concerns about hallucinations. While prior work has evaluated LLMs extensively in news domains, most evaluation of dialogue summarization has focused on BART-based models, leaving a gap in our understanding of their faithfulness. Our work benchmarks the faithfulness of LLMs for dialogue summarization, using human annotations and focusing on identifying and categorizing span-level inconsistencies. Specifically, we focus on two prominent LLMs: GPT-4 and Alpaca-13B. Our evaluation reveals subtleties as to what constitutes a hallucination: LLMs often generate plausible inferences, supported by circumstantial evidence in the conversation, that lack direct evidence, a pattern that is less prevalent in older models. We propose a refined taxonomy of errors, coining the category of "Circumstantial Inference" to bucket these LLM behaviors and release the dataset. Using our taxonomy, we compare the behavioral differences between LLMs and older fine-tuned models. Additionally, we systematically assess the efficacy of automatic error detection methods on LLM summaries and find that they struggle to detect these nuanced errors. To address this, we introduce two prompt-based approaches for fine-grained error detection that outperform existing metrics, particularly for identifying "Circumstantial Inference."