I have the Sims 3 base game. I've tried downloading it dozens of times, but it just won't download. I just got this Macbook Pro in August 2011.
I insert the disc and click the DVD icon on my desktop. It brings up the window with the Sims 3 Installer icon. I click on the icon, and the window to install the game pops up.
But, then the window freezes on 'Verifying installer.'

Am I doing something wrong? Why won't it install?

Bad disk ? maybe a faulty optical drive? Your Mac is still under warranty so I'd take it to the Apple store. As for the disk, see if it works on another Mac. If not maybe you can return it.

Looks like a lot of problems with TS3 on the Mac - http://forum.thesims3.com/jforum/posts/list/413974.page

My take on this is that TS3 seems to work best on Windows, so Boot Camp is certainly an option, rather than wait for EA to fix TS3 on new Macs.