I have a piece of music, and it plays through my Mac 100% fine. But, after importing it into Final Cut Pro it develops some 'blipping', and this is also present after rendering.

Listen to the music track here, and you'll see for yourself:

Portland Apartments on Vimeo (http://vimeo.com/6200955)

The music is fine, it only goes wrong after being sent to Final Cut.

Any suggestions?

Try converting the audio to AIFF first. I'm guessing the original was MP3, and FCP doesn't like MP3s all that much. A simple way to convert one file is to use iTunes.

A simple way to convert one file is to use iTunes.

Or alternatively (I find this a little easier): take the MP3 into QuickTime Player, Hit Cmd-E to export, choose "to AIFF", and the first time you do this, check the options are set to 16 bit stereo 48 KHz, best quality.

I've had perfect (well, perfect as MP3s tend to be) results this way.

The clicking may be to do with the mismatch between the common 44.1 KHz and the required 48 KHz rounding that FCP's doing rather than the careful padding that QTP does.

IMHO.