Thanks to Twitter, you can find every song that gets played on Beats 1.
Here's a scenario you might find familiar. You're listening to Beats 1 when a great song comes on that you haven't heard before. You try to add it to your collection but it's not available. You search the iTunes Store but it's not there either. In the meantime, the song is over. What was it again? Drat, I forgot. Oh well.
I was complaining about this on Twitter this morning when Kristoffer Tsinontas pointed me to the Twitter account Beats1 Plays. This unofficial account live-tweets every track that's being played on Beats 1. In the scenario above, I could simply hop on Twitter and see the very song I missed.
Regarding those songs we can't add to our libraries, I'm not sure if that's a bug or if these songs aren't available for streaming (or some combination of both). In the meantime, Beats1Plays will at least let you make a record of what you've missed.