There are many faithful LDS podcasts out there. I’ll list a few:
1) Laura Hales is a great host at LDS Perspectives. She regularly introduces extremely faithful and authoritative guests on a huge range of topics:
A recent LDS Perspectives podcast:
Episode 103: The Need for Historicity of the Book of Mormon with Stephen Smoot
2) FAIR Mormon has been producing podcasts and other materials for many, many years.
3) The Maxwell Institute is very scholarly, and produces another great podcast.
The current MI podcast: #89–‘Sister Saints,” with Colleen McDannell
4) Gospel Tangents is a very active and informative YouTube channel.
From the “About” section on their YouTube channel:
Here at Gospel Tangents, we explore Mormon History, Science, and Theology. We don’t shy away from anything: polygamy, the racial ban, Mountain Meadows Massacre, the Mark Hoffman bombings, Masonry, DNA & the Book of Mormon, multiple First Vision accounts. It’s all fair game. If you want us to talk about something, please let us know!
We welcome all flavors of Mormons: active, inactive, former Mormons, the Community of Christ–anyone who has an interest in the restoration of the gospel that Joseph Smith restored in 1830. We want a 360 degree view of Mormonism. Of course we’ll talk to LDS Scholars, Brian Hales, Paul Reeve, Mark Staker, and Ugo Perego but we’ll also talk to people like Lach MacKay, an apostle for the Community of Christ, Jim Vun Cannon, a counselor in the First Presidency of the Remnant Church of Jesus Christ of Latter Day Saints, Anne Wilde, David Rosenvall who has an unusual geography theory. Please subscribe and tell us what you’d like to learn more about!
5. Exploring Mormon Thought by Blake Ostler. Blake is a SLC attorney who has long engaged in philosophy and religion.
Extremely bright thinker and wonderful human being.
6) The Interpreter Radio Show can be heard Sunday evenings from 7 to 9 PM (MST) on K-TALK, AM 1640, or you can listen live on the Internet at ktalkmedia.com.
Call in to 801-254-1640 with your questions and comments during the live show.
7) Van Hale has been defending the Church for over 30 years on his radio program Mormon Miscellaneous.