Chromosomal 16p11.2 deletion syndrome frequently presents with intellectual disabilities, speech delays, and autism. Here we investigated the Dolmetsch line of 16p11.2 heterozygous (+/-) mice on a range of cognitive tasks with different neuroanatomical substrates. Robust novel object recognition deficits were replicated in two cohorts of 16p11.2 +/- mice, confirming previous findings. A similarly robust deficit in object location memory was discovered in +/-, indicating impaired spatial novelty recognition. Generalizability of novelty recognition deficits in +/- mice extended to preference for social novelty. Robust learning deficits and cognitive inflexibility were detected using Bussey-Saksida touchscreen operant chambers. During acquisition of pairwise visual discrimination, +/- mice required significantly more training trials to reach criterion than wild-type littermates (+/+), and made more errors and correction errors than +/+. In the reversal phase, all +/+ reached criterion, whereas most +/- failed to reach criterion by the 30-d cutoff. Contextual and cued fear conditioning were normal in +/-. These cognitive phenotypes may be relevant to some aspects of cognitive impairments in humans with 16p11.2 deletion, and support the use of 16p11.2+/- mice as a model system for discovering treatments for cognitive impairments in 16p11.2 deletion syndrome.