Many previous studies have shown that peer assessment teaching can help develop cognitive skills. There are also numerous studies that explore issues related to web-based peer assessment activities. However, most current studies focus on peer assessment instructional activities under an asynchronous collaborative learning environment. In turn, there is a lack of research related to the interactive process of synchronous peer assessment activities and the cognitive dimensions of the discussion. Therefore, this study conducts an empirical analysis of an instructional activity in which 38 students used online instant messaging tools to conduct peer assessments. Students viewed and evaluated each other’s work on a one-to-one basis. This case study uses the cognitive processing dimensions from Bloom’s Taxonomy to analyze the contents of the discussions. Quantitative content analysis, lag sequential analysis, and qualitative content analysis were conducted during the study to explore the cognitive dimensions of peer assessment, both the characteristics and limitations of interactive behavioral patterns, and the differences in discussion patterns between high- and low-quality discussion groups. The results show that synchronous peer assessment discussions can elicit a two-way interaction between basic and advanced cognitive dimensions, which may be valuable in developing cognitive abilities. However, the results also show a lack of advanced cognitive dimensions and a tendency for the discussion to repeatedly go off-topic in the observed discussion. After examining the results, we propose relevant recommendations and references for teachers and researchers interested in synchronous peer assessment instructional activities.