My new alto sounded flat when played alongside a tutorial CD. I rectified this by pushing the mouthpiece further on to the cork tip of the crook. It worked, but is this normal? It seems a bit random to me - a millimetre either way and it could be out again. Any advice, anyone?

How does that match up with your tuner?

<Added>

What is the frequency or how many cents off is the CD?

Phew! I'm a novice, mate - you've rather lost me there. I can test the saxophone pitch against my (electric) piano, so that's OK. The main question is: should the precise position of the mouthpiece on the crook affect the pitch? Do I have to judge it to the millimetre every time I put it on ready to play? Surely that's leaving to much to guesswork.

Oh, I see your question now.
The answer is YES! Tuning is very exact. A difference of a half a millimeter will have an affect on your pitch. But don't let that bother you. It will allow you to adjust more easiliy with others.

That's a relief - not a rogue instrument, just learner's inexperience. Thanks for your help.