Typically, the composition copyright for a recorded piece of music is held by a group like ASCAP or BMI, and the performance copyright for that same piece of music is held by the record label. The permissions required, from whom, and the associated costs (some are government-set and others are negotiated) to use a single piece of music, or to obtain a license for a library of music, all vary depending on the type of transmission (over-the-air broadcast [WFMU], digital streaming [WFMU's archived shows, The Best Show's live broadcast], digital download [The Best Show podcast], etc.). To use a song in a podcast, one would need permission from holders of both types of copyrights for "reproduction rights" and *probably* "public performance rights".
(WFMU had an unsanctioned backdoor to download full episodes inclusive of music, which is why there are mp3s of complete The Best Show on WFMU episodes.)To cover the of the other points in this thread:
- If your podcast app does not have The Best Show listed, there is usually a way to add a show by pasting in its RSS feed. The Best Show's feed is this address: http://thebestshow.libsyn.com/rss
- For streaming on Android, this is still a shit situation. You have to download the VLC app, then tune into The Best Show's Twitter feed (@bestshow4life) around showtime when it posts a URL ending in ".m3u8", then copy that address, then open VLC, then click on the "Open network stream" icon (second from right at the top on the main screen), then paste that address, then click "Open". You will want to keep the address on your clipboard or in a note on your phone if/when the stream drops.