First of all, I'd really like to thank BlueBellFlora for all the work, time and patience that she has put into researching and putting together many tips and tricks for the Mac users. This is a Mac user's Best Friend. Read this thread before posting any problems and I'm sure you'll find an answer to your question or concern. Caspinwall, itsaprilXD and tamalinn also have contributed to this thread and many guides other as well.
The next thread is from caspinwall and details problems and solutions with using Origin. Yes, Origin does work on the Mac side. Yes, it is your best friend if you lose your disk and have registered your game. If there is a problem with a game not showing up in your Origin account and you have registered it, you will need to contact EA support.
And lastly not to toot my own horn, here is a thread about how to patch your game correctly and safely. I am patched to the current patch 1.67 and run all of the EP's and SP's as well as a lot of Store items and sets. My game is stable and runs fine. I haven't tried to run it on high graphics settings lately, but I'm sure it will run fine.
If you are trying to play Sims 3 on a newer Macbook, here is a list of the new Macs which have the Iris Intel Graphics cards. Please be advised that Sims 3 does NOT recognize this brand of graphics card and you may experience weird graphics or the game may not start at all. There is a workaround since Sims 3 will never be updated again.