I was listening to Blackbird from the third Anthology album last night, and I noticed a tapping sound in the background keeping the beat that I haven't really picked up on before. I'm not sure what take it was, but as far as I know it was just Paul singing and playing guitar in that song without anyone else. Does anyone know what that sound is? It's not a drum, I can tell that by the sound...is Paul tapping his foot or something?

From songfacts.com:
Only 3 things were recorded: Paul's voice, his acoustic guitar, and a tapping. According to the video The Complete Beatles, the tap was not a foot or metronome - the Master was intentionally scratched. If you listen closely you will notice that is sounds like a scratch on a record. Birds were dubbed in later.

There's a video of Paul doing a demo of Helter Skelter and singing Blackbird at the studio (Sir George can be seen too) and you can hear the same sound made by his feet ...

I can't find it   ... only the Helter Skelter demo:
http://youtube.com/watch?v=QuNV5O1qEPI

I firmly believe it was Paul tapping his feet (i always have)