Is it just my hearng? or is the quality of downloaded music from ITunes not good?

I have found some music sounding as if the 'turntable' is varying in its speed causing distortion of the sound.

Does the speed of the download affect the resultant download?

It has to be your player. No matter what the download speed is, even it is stopped in between, has no impact on the speed after the download whatsoever.

Try another player (VLC Media Player for example) and see if it still exists.

Your download speed has nothing to do with it.

Generally the quality is good - that said if your hearing is "odd" then you might be able to hear compression artifacts. For people with normal hearing it's impossible to hear the difference between a high quality compressed song and a CD. But because the compression is based on normal human hearing, people who "hear different" from normal do hear differences.

Other than that, there's always the possibility of bugs...