Hello again,
I don't think that buying another expansion would help you, although it's your choice of course. The reason I think it won't help is that the patch that came with the final expansion (ITF) was 1.63 and the latest one was 1.66, which you'd have to get through the Launcher or superpatch anyway. So adding any more expansions beyond those that you already have would not give you any advance on the patch level that you can already get.
Also, although it's a good idea to get patched up to date, the original issue that is preventing you from playing actually seems to be with your current disc rather than the patch. It is still possible that the disc is simply damaged and cannot be recognised by the game, but unless the store that sold it to you is willing to give you a replacement, there's not much you can do about that.
Instead of buying another expansion, I would suggest trying Origin. I personally have developed a hatred of Origin as it seems to go wrong, but seeing as your game's not working anyway, you don't have much to lose!
If you have Time Machine for your Mac, you should first run that to make a backup in case you want to go back.
Uninstall your last expansion pack (Island Paradise) using the uninstaller and by trashing any transgaming files for Island Paradise using the instructions in BluebellFlora's guide (BUT don't trash the others unless you want to uninstall the whole thing). http://bluebellflora.com/the-sims-3-on-a-mac/how-to-do-a-clean-uninstall-and-reinstall-on-a-mac/
Once you've got rid of the disc-dependent version of the installation, you can register the code with Origin and download it from there. I will paste instructions below on how to have the best chance of success doing this. If you can get it installed through Origin then the disc will not longer matter as you won't need one to play.
To download and install games through Origin:
First install the Origin client for Mac and make sure it is up-to-date. The latest version can be downloaded from here: http://www.dm.origin.com/mac/download
Additional advice on how to download games (thank you Tremayne for this tip):
When downloading from Origin, do NOT use the first install icon. Move your cursor over the game cover and click on the information (letter i) and then click on the install button from there.
For some reason, downloads from Origin frequently become corrupted. Using the i reduces the chance of your download being corrupted. If you have already been unfortunate and have a corrupted download, then it is important to remove all traces of this before trying again, by doing a thorough, clean uninstallation first.
I wish you the best of luck. This game is frustrating at the best of times and especially so on a Mac!
Caspin