Since Apple released OS X v10.7 due a changes is operating system older Blizzard games like Warcraft 3 are no longer supported (aka working) on OS X v10.7+.
You can read more about this issue here.
Poop_Soup from /r/WC3 subreddit have found a solution how to install Warcraft 3 on Mac OS X v10.7 or newer.
Here's what you will need:
-A copy of Warcraft 3 (Mac)
-Access to a Mac running 10.6 (Snow Leopard) or lower.
Install wc3 on that computer(10.6) and download the most recent update. Then drag the wc3 folder, found in your applications, onto a hard drive or thumb drive. Then drag that folder into your applications folder on your mac (running 10.7 or 10.8.) Open up that folder and run the application. BOOM. You are now playing wc3 again.
ALSO, if you still have snow leopard or lower with wc3 installed, you should be totally fine when upgrading to lion and mountain lion, because, again, it's the installer that is not compatible NOT the application itself.
I don't have a Mac so i can't test this solution. If you have any question or issues check Reddit post at /r/WC3 subreddit: