Comparative psychology assesses cognitive abilities and capacities of non-human animals and humans. Based on performance differences and similarities in various species in cognitive tests, it is inferred how their minds work and reconstructed how cognition might have evolved. Critically, such species comparisons are only valid and meaningful if the tasks truly capture individual and inter-specific variation in cognitive abilities rather than contextual variables that might affect task performance. Unlike in human test psychology, however, cognitive tasks for non-human primates (and most other animals) have been rarely evaluated regarding their measurement validity. We review recent studies that address how non-cognitive factors affect performance in a set of commonly used cognitive tasks, and if cognitive tests truly measure individual variation in cognitive abilities. We find that individual differences in emotional and motivational factors primarily affect performance via attention. Hence, it is crucial to systematically control for attention during cognitive tasks to obtain valid and reliable results. Aspects of test design, however, can also have a substantial effect on cognitive performance. We conclude that non-cognitive factors are a minor source of measurement error if acknowledged and properly controlled for. It is essential, however, to validate and eventually re-design several primate cognition tasks in order to ascertain that they capture the cognitive abilities they were designed to measure. This will provide a more solid base for future cognitive comparisons within primates but also across a wider range of non-human animal species.