Yes the Playstation does take podcasts, I think there is a page for podcast content for the console, and it does list some of Mormon Channel's material. In the discussion over the Roku device it was found that there is a page that shows some content available on the web, and that showed a number of Mormon Channel program titles.
But apps for web-enabled TV and devices are the next thing, some have already been mentioned, and any development for the devices will have to take into account the specific requirements of each device. One report I saw puts Pandora on at least 200 devices already or known to be in the works.
Auto manufacturers like Ford, Toyota, and BMW are offering in-car Internet, and will need the apps to add voice-recognition features to fit their systems, this is so the driver can simply call up the program or station, it's already being done for Pandora, and a few others, and the need to develop for these in-car systems is going to be significant. A study on radio usage says the average American radio user listens 20 hours or so a week, over 8 hours of that in the car. Some do it a lot more, especially if they travel around a lot, and a few do it much less, especially if they do not drive a lot or have to go very short distances, so needs will vary.
As to BYUTV, I have noticed a playlist on Mormon Channel's Youtube page listing some BYUTV generated/produced content already, that makes it possible for at least some items right from Youtube, but accessing BYUTV's other content will require a separate app or routine within an app I think.