Remember shadow reading? It’s a funny way to improve your students‘ pronunciation; have them listen to a dialog and assign a specific task to them; e.g. fill in the missing words or something similar; when all students have the correct version of the dialog play it again. Assign Speaker A to one half of the group and Speaker B to the other half of the group and have the students read along with the recording. To make the task a bit more kinesthetic have the students stand up whenever their part comes up.
This is not a podcast specific task but I have found the ELT podcast useful for this task; the podcast features Theme-based conversations and language practice for students of English, such as EFL, ESL and ESOL. The dialogs have two or more speakers and the mp3 files include a transcript; for levels beginner – university students.