Recent research has leveraged peer assessment as a grading system tool where learners are involved in learning and evaluation. However, there is limited knowledge regarding individual differences, such as personality, in peer assessment tasks. We analyze how personality factors affect the peer assessment dynamics of a semester-long remote learning course. Specifically, we investigate how psychological constructs shape how people perceive user-generated content, interact with it, and assess their peers. Our results show that personality traits can predict how effective the peer assessment process will be and the scores and feedback that students provide to their peers. In conclusion, we contribute design guidelines based on personality constructs as valuable factors to include in the design pipeline of peer assessment systems.