This paper studies the problem of learning a control policy without the need for interactions with the environment; instead, learning purely from an existing dataset. Prior work has demonstrated that offline learning algorithms (e.g., behavioural cloning and offline reinforcement learning) are more likely to discover a satisfactory policy when trained using high-quality expert data. However, many real-world/practical datasets can contain significant proportions of examples generated using low-skilled agents. Therefore, we propose a behaviour discriminator (BD) concept, a novel and simple data filtering approach based on semi-supervised learning, which can accurately discern expert data from a mixed-quality dataset. Our BD approach was used to pre-process the mixed-skill-level datasets from the Real Robot Challenge (RRC) III, an open competition requiring participants to solve several dexterous robotic manipulation tasks using offline learning methods; the new BD method allowed a standard behavioural cloning algorithm to outperform other more sophisticated offline learning algorithms. Moreover, we demonstrate that the new BD pre-processing method can be applied to a number of D4RL benchmark problems, improving the performance of multiple state-of-the-art offline reinforcement learning algorithms.