Teachers' ability to accurately judge difficulties of mathematical tasks is an essential aspect of their diagnostic competencies. Although research has suggested that pedagogical content knowledge (PCK) is positively correlated with the accuracy of diagnostic judgments, experimental studies have not been conducted to investigate how PCK affects perception and interpretation of relevant task characteristics. In an intervention study with a control group, 49 prospective mathematics teachers judged the difficulty of 20 tasks involving functions and graphs while an eye tracker tracked their eye movements. Some of the tasks included characteristics well known to be difficult for students. Participants' domain-specific PCK of typical student errors was manipulated through a three-hour intervention, during which they learned about the most common student errors in function and graph problems. We found that the process of perception (relative fixation duration on the relevant area in the tasks) was related to judgment accuracy. Pre-post comparisons revealed an effect of the intervention not only on participants' domain-specific PCK of typical student errors but also on their perception and interpretation processes. This result suggests that domain-specific PCK of typical student errors allowed participants to focus more efficiently on relevant task characteristics when judging mathematical task difficulties. Our study contributes to our understanding of how professional knowledge makes teachers' judgment processes of mathematical tasks more efficient.