For years bootlegs (LPs back then, the "Live at the Beeb" series) of the BBC-radioshows were in high demand: they covered every show the Fab Four ever performed for the BBC. They would never fit on a 2CD-set. So yes, one will miss a song or two on this collection, but there are some real gems (I'll be on my way, Clarabella, Lucille - to name but three). I think they could have put on more covers that were not released on their official albums, as some performances are clearly inferior.
The BBC itself did not archive these recordings, as far as I know, though there may be acetates. Luckily most of it was recorded by fans and survived that way. Naturally the audio quality of these recordings is far from perfect (compared to their first album, which in itself was almost 'live in the studio'), but most are listenable enough. Some are really bad (Keep your hands off my baby, for one, and a couple of TV performances), but I guess these are included for their uniqueness. I could have done without the chats, especially when they are edited over the music and you can't skip the track.
All in all it's a great set that shows the Beatles'influences and for me, I think some of their covers are so much better than the originals!