Some clips have special requirements to allow them to play (e.g. from Zombies, Run! Season 2 onwards). For example, some clips require you to have played a certain episode or mission in that season, while other clips will only trigger on certain days or if other clips have been unlocked.
Because of this, you'll find that some Radio Mode clips will remain locked, even if you have been given the mission complete message. If you restart radio mode from the beginning though, you should be able to hear and unlock some of the other clips.