For Mac simmers having this problem, please see the first post of the main Mac help thread:
http://answers.ea.com/t5/The-Sims-3/Links-to-Mac-help-threads-and-guides/td-p/749664
Try the tips under 'primary things to try first'.
I see that some folk have tried reinstalling the game. So, if all else fails and you decide to reinstall, be sure to cleanly uninstall first. When you uninstall TS3 games on your Mac using the uninstaller, the game leaves behind stray files and isn't completely removed from your computer. These files may conflict with future installations. It is best to completely remove them. BluebellFlora's website provides a guide on how to do this:
http://bluebellflora.com/the-sims-3-on-a-mac/how-to-do-a-clean-uninstall-and-reinstall-on-a-mac/
After cleanly uninstalling, install the base game and patch it up to date. If you cannot update via the Launcher, download and apply the latest cumulative manual patch (called the superpatch) for Mac.
Check that your game works properly. Then install any EPs and SPs that you own, in order of release date.