I've owned several Apple Cinema Displays over the years: 2 - 24" ACD's, 2 - 27" ACD's, and a Thunderbolt Display.
Out of all of them, I've had one 24" ACD that had intermittent ticking issues. The ticking is audible, random, and persistent.
After reading some forums, they are somewhat common problems.
It is definitely annoying, so much so that I ended up selling that one since it was outside the warranty period.