As large language models (LLMs) often generate plausible but incorrect content, error detection has become increasingly critical to ensure truthfulness. However, existing detection methods often overlook a critical problem we term as self-consistent error, where LLMs repeatly generate the same incorrect response across multiple stochastic samples. This work formally defines self-consistent errors and evaluates mainstream detection methods on them. Our investigation reveals two key findings: (1) Unlike inconsistent errors, whose frequency diminishes significantly as LLM scale increases, the frequency of self-consistent errors remains stable or even increases. (2) All four types of detection methshods significantly struggle to detect self-consistent errors. These findings reveal critical limitations in current detection methods and underscore the need for improved methods. Motivated by the observation that self-consistent errors often differ across LLMs, we propose a simple but effective cross-model probe method that fuses hidden state evidence from an external verifier LLM. Our method significantly enhances performance on self-consistent errors across three LLM families.