The Force Concept Inventory (FCI) has been widely used to assess student understanding of introductory mechanics concepts by a variety of educators and physics education researchers. One reason for this extensive use is that many of the items on the FCI have strong distractor choices which correspond to students' alternate conceptions in mechanics. Instruction is unlikely to be effective if instructors do not know the common alternate conceptions of introductory physics students and explicitly take into account students' initial knowledge states in their instructional design. Here, we discuss research involving the FCI to evaluate one aspect of the pedagogical content knowledge of teaching assistants (TAs): knowledge of introductory student alternate conceptions in mechanics as revealed by the FCI. For each item on the FCI, the TAs were asked to identify the most common incorrect answer choice of introductory physics students. This exercise was followed by a class discussion with the TAs related to this task, including the importance of knowing student difficulties in teaching and learning. Then, we used FCI pretest and post-test data from a large population (~900) of introductory physics students to assess the extent to which TAs were able to identify alternate conceptions of introductory students related to force and motion. In addition, we carried out think-aloud interviews with graduate students who had more than two semesters of teaching experience in recitations to examine how they reason about the task.We find that while the TAs, on average, performed better than random guessing at identifying introductory students' difficulties with FCI content, they did not identify many common difficulties that introductory physics students have after traditional instruction. We discuss specific alternate conceptions, the extent to which TAs are able to identify them, and results from the think-aloud interviews that provided valuable information about why TAs sometimes select certain alternate conceptions as the most common, which are instead very rare among introductory students. We also briefly compare the performance of the TAs with physics instructors in identifying common introductory student difficulties with FCI content using the same task and find that their performances are comparable. Furthermore, our data suggest that the ability to identify introductory students' difficulties was not correlated with whether the TAs obtained their undergraduate degree in the U.S. or elsewhere.