Background Problematic alcohol use is associated with neuropsychological consequences, including cognitive biases. The goal of the study was to explore the moderating role of executive control and readiness to change on the relationship between alcohol use and cognitive biases in light and problematic drinkers with and without mild to borderline intellectual disability (MBID). Method Participants (N = 112) performed the visual dot probe task to measure the strength of the cognitive biases. Executive control was measured using two computerised tasks for working memory capacity (Corsi block‐tapping task) and inhibitory control (Go/No‐go task). Readiness to change was measured using the Readiness to Change Questionnaire. Results No cognitive biases or executive dysfunctions were found in problematic drinkers. Working memory capacity and inhibitory control were impaired among individuals with MBID, irrespective of severity of alcohol use‐related problems. Executive control and readiness to change did not moderate the relationship between alcohol use and cognitive biases. Conclusion The results fail to support the dual‐process models of addiction, but results need to be treated with caution given the problematic psychometric qualities of the visual dot probe task. Implementing a neurocognitive assessment and protocols in the treatment of substance use disorders seems premature.