Despite the best efforts of the security community, security vulnerabilities in software are still prevalent, with new vulnerabilities reported daily and older ones stubbornly repeating themselves. One potential source of these vulnerabilities is shortcomings in the used language and library APIs. Developers tend to trust APIs, but can misunderstand or misuse them, introducing vulnerabilities. We call the causes of such misuse blindspots. In this paper, we study API blindspots from the developers' perspective to: (1) determine the extent to which developers can detect API blindspots in code and (2) examine the extent to which developer characteristics (i.e., perception of code correctness, familiarity with code, confidence, professional experience, cognitive function, and personality) affect this capability. We conducted a study with 109 developers from four countries solving programming puzzles that involve Java APIs known to contain blindspots. We find that (1) The presence of blindspots correlated negatively with the developers' accuracy in answering implicit security questions and the developers' ability to identify potential security concerns in the code. This effect was more pronounced for I/O-related APIs and for puzzles with higher cyclomatic complexity. (2) Higher cognitive functioning and more programming experience did not predict better ability to detect API blindspots. (3) Developers exhibiting greater openness as a personality trait were more likely to detect API blindspots. This study has the potential to advance API security in (1) design, implementation, and testing of new APIs; (2) addressing blindspots in legacy APIs; (3) development of novel methods for developer recruitment and training based on cognitive and personality assessments; and (4) improvement of software development processes (e.g., establishment of security and functionality teams).