How to search collection of podcasts (.mp3 files)?
Transcribe then topic model the recordings. This will let you know which podcast talks about the subject of interest, then you can search the transcript. If you really need it to pinpoint the moment when the subject was discussed, you'll need a temporal topic model like so but that would add a good bit of complexity.

Google has a good service for the first part. You can use an open source library like gensim for the second part.