Can we detect plagiarism from/in a podcast?
I doubt that anything currently exists. I don't, however, think the problem is infeasible. But it is very hard.
First, plagiarism is about ideas, not words. One can plagiarize without using any of the original words. Second, plagiarism is about the creation of the ideas and claiming them as your own. Both of these are difficult problems.
First, one would probably need both things to be in a common format, probably written language. This part currently has solutions that mostly work, but it is the easiest part. Second, the actual meaning of the words would need to be extracted and probably also structured in some way.
Finally, the system would need to watch out that the ideas weren't just being expressed but were being claimed. I can certainly speak and write about relativity without plagiarizing Einstein.
I think it would be an interesting research problem, but I also think that it would be pretty far in the future before such a system could eliminate most of the false positives and false negatives.
A data driven AI system might be the way to attack it, but these are still subject to many false decisions.
But it needs to be an intelligent agent to make the call. A person can use transcripts and understand the meaning and the intent. A sufficiently sophisticated AI might also be able to do it, but it is still a bit beyond where were are, especially if you require a low fault rate.

Copyright is easier, since it is about words (pictures, sounds, etc).
Likewise, students copying things to cheat is generally easier since they will most likely be copying words rather than extracting the ideas/semantics from the words and there is an implicit assumption that the intent is that the ideas are their own.