Does Apple change OS X operating systems between the GM and the final release? For instance, I've found quite a few bugs while working with the Mountain Lion Golden Master. Is there any chance Apple might fix these in the public release?

Thanks!
There's a first time for everything but, but basically: no.

Unless you have found the mother of all security bugs, so humiliating that it would overshadow Apple's entire Mountain Lion release, the bug to end all bugs and live on in infamy, it just is not going to happen.

Not to mention, fixing and testing bugs generally takes time. The fastest Apple bug fix ever, to my knowledge, took two days but that's very unusual for a company its size. In general it takes weeks, in many cases months, even years.