Background: The behavioural symptoms of autism spectrum disorder (ASD) are thought to reflect underlying cognitive deficits/differences. The findings in the literature are somewhat mixed regarding the cognitive features of ASD. This study attempted to address this issue by investigating a range of cognitive deficits and the prevalence of multiple cognitive atypicalities in a large population-based sample comprising children with ASD, their unaffected co-twins, and typically developing comparison children. Methods: Participants included families from the Twins Early Development Study (TEDS) where one or both children met diagnostic criteria for ASD. Overall, 181 adolescents with a diagnosis of ASD and 73 unaffected co-twins were included, plus an additional 160 comparison control participants. An extensive cognitive battery was administered to measure IQ, central coherence, executive function, and theory of mind ability. Results: Differences between groups (ASD, co-twin, control) are reported on tasks assessing theory of mind, executive function, and central coherence. The ASD group performed atypically in significantly more cognitive tasks than the unaffected co-twin and control groups. Nearly a third of the ASD group presented with multiple cognitive atypicalities. Conclusions: Multiple cognitive atypicalities appear to be a characteristic, but not universal feature, of ASD. Further work is needed to investigate whether specific cognitive atypicalities, either alone or together, are related to specific behaviours characteristic of ASD.