Static bug finders have been widely-adopted by developers to find bugs in real world software projects. They leverage predefined heuristic static analysis rules to scan source code or binary code of a software project, and report violations to these rules as warnings to be verified. However, the advantages of static bug finders are overshadowed by such issues as uncovered obvious bugs, false positives, etc. To improve these tools, many techniques have been proposed to filter out false positives reported or design new static analysis rules. Nevertheless, the under-performance of bug finders can also be caused by the incorrectness of current rules contained in the static bug finders, which is not explored yet. In this work, we propose a differential testing approach to detect bugs in the rules of four widely-used static bug finders, i.e., SonarQube, PMD, SpotBugs, and ErrorProne, and conduct a qualitative study about the bugs found. To retrieve paired rules across static bug finders for differential testing, we design a heuristic-based rule mapping method which combines the similarity in rules description and the overlap in warning information reported by the tools. The experiment on 2,728 open source projects reveals 46 bugs in the static bug finders, among which 24 are fixed or confirmed and the left are awaiting confirmation. We also summarize 13 bug patterns in the static analysis rules based on their context and root causes, which can serve as the checklist for designing and implementing other rules and or in other tools. This study indicates that the commonly-used static bug finders are not as reliable as they might have been envisaged. It not only demonstrates the effectiveness of our approach, but also highlights the need to continue improving the reliability of the static bug finders.