The 'Run' button was always flaky for me back when I was actually able to use Coldstone, especially under the Carbon client. Basically, it was hit and miss as to whether I'd get a compiled version of the game to test through, or whether I'd end up with a crashed CGE. It's on the 'known bugs list' if I remember correctly.
As a try-and-fix though, I'd suggest digging up and trashing your CS preferences files, and seeing if that makes a difference. If not, I'd advise just sticking to 'build' rather than run. Oh, and make sure you're not opening the newly built app in OSX, but in Classic - I'm afraid I can't remember if Coldstone defaults to building a Carbon binary or not, and I'm not sure where my CS CD is right now or I'd check.
But yes - try the preferences delete-then-reboot trick, otherwise I'd just say it's another issue that will just have to be worked around.