Hi
Are you launching the game from Origin or from the actual game file in Applications on your Mac?
Sometimes Origin downloads are corrupted - it happens frequently unfortunately - so if your Uni Life isn't working correctly you may need to uninstall and reinstall.
But first some checks. Is your game patched up to date? It sounds as though you are getting a message about patching - if you cannot patch through the Launcher you can use the manual superpatch - a lot of simmers find this is more successful. The links to download the Mac patch for all the various regions, as well as instructions on how to do it, are provided here: http://forum.thesims3.com/jforum/posts/list/549552.page
Did you have any problems with the Uni Life installation (can you see the icon is highlighted at the bottom of the Launcher and do you see the shortcut icon for Uni Life when you look in Applications/TheSims3)?
Have you removed all custom content and mods to see if any are affecting it?
Have you tried the tips under "primary things to try first" on the main Mac thread, to see if a freshly generated folder will solve the problem:
http://answers.ea.com/t5/The-Sims-3/Links-to-Mac-help-threads-and-guides/m-p/749664#U749664
If all else fails you can simply uninstall and reinstall the whole game so don't worry too much.
Caspin