The Test of Understanding Graphs in Kinematics (TUG-K) is a multiple choice test developed by Beichner to assess students' understanding of kinematics graphs. Many of the items on the TUG-K have strong distractor choices which correspond to introductory students' common difficulties with kinematics graphs. Instruction is unlikely to be effective if instructors do not know these common difficulties and take them into account in their instructional design. We evaluate the performance of first year physics graduate students at identifying introductory students' common difficulties related to kinematics graphs. In particular, for each item on the TUG-K, the graduate students were asked to identify which incorrect answer choice they thought would be most commonly selected by introductory physics students if they did not know the correct answer after instruction in relevant concepts. We used the introductory student data from Beichner's original paper to assess graduate students' knowledge of introductory students' difficulties. Furthermore, we selected the four questions on the TUG-K on which the graduate student performance was the poorest for a more detailed analysis which included think-aloud interviews. We present results which can partly account for the poor graduate student performance on these questions and also inform instruction in professional development courses.