With the recent release of Mac OS X 10.8 Mountain Lion, all Mac applications are required to be signed by a developer registered with Apple, otherwise it won't work out-of-the-box. This new feature in Mountain Lion is called Gatekeeper, and gives Apple a way to stop spyware and other nasty stuff from spreading.
Because of this, we recommend keeping Gatekeeper enabled, and we've produced an updated build of Mixxx 1.10.1 that's signed so it should work on Mountain Lion:
In the near future, we'll be working to change our release process so all packages are signed, meaning there won't be a specific version for Mountain Lion. Thanks to our build server, we're now able to create Mixxx releases automatically, but it still requires a fair amount of work to keep it working because Mixxx changes so fast. It's also a bit of a headache to distribute our packages to all of our mirrors, so we'll try to improve that as well.
In the meantime, enjoy, and please file bugs if you run into any problems on Mountain Lion!