OpenStreetMap (OSM), with its global coverage and Open Database License, has recently gained popularity. Its quality is adequate for many applications, but since it is crowd-sourced, errors remain an issue. Errors in associated tags of the road network, for example, are impacting routing applications. Particularly road classification errors often lead to false assumptions about capacity, maximum speed, or road quality, possibly resulting in detours for routing applications. This study aims at finding potential classification errors automatically, which can then be checked and corrected by a human expert. We develop a novel approach to detect road classification errors in OSM by searching for disconnected parts and gaps in different levels of a hierarchical road network. Different parameters are identified that indicate gaps in road networks. These parameters are then combined in a rating system to obtain an error probability to suggest possible misclassifications to a human user. The methodology is applied to an exemplar case for the state of New South Wales in Australia. The results demonstrate that (1) more classification errors are found at gaps than at disconnected parts, and (2) the gap search enables the user to find classification errors quickly using the developed rating system that indicates an error probability. In future work, the methodology can be extended to include available tags in OSM for the rating system. The source code of the implementation is available via GitHub.