Well, that's not an easy request.
MSA is used as a spoken language in news, documentaries, children anime, some songs (uncommon), and some movies & series (rare). Most of the time MSA is influenced by a dialect; given the fact that it's not spoken by Arabs in any country. So unless you are watching a very professional news anchor or children cartoon (manga or anime) dubbed in MSA; it's highly unlikely that you find a pure MSA podcast.
Anyway, depending on your interests you may find one of these helpful:
- ArabicPod 101 - Listening Practice
A playlist of 85 videos in MSA, from beginner to advanced level. They are short videos with some small stories and some questions about what you understand from what you hear. The first 77 videos are the sole lessons; each of 2.5 min average. The last 8 videos are different collections of the same individual lessons.
- If you are a news/documentary person:
BBC (news & documentary)
Al Jazeera (news)
Al Jazeera Documentary
France 24 (news & culture)
DW (news & culture)
Be careful here that only the anchor/the narrator will be speaking in MSA. All these channels have a live broadcast except Nat Geo, but it's the only documentary channel inhere with 90% of its content in MSA (originally in a foreign language, so the whole video is dubbed in MSA).
Unfortunately, I didn't find any complete playlist for some cartoons. However, you can see the opening credits songs for some of popular cartoons (in my childhood) here:
Songs & movies are another story.