Ok, I tried another account and I get the same problem... there doesn't seem to be any specific error code that I can see (but then, I'm not particularly computer code literate), although the error report begins with:
Process: tgInstall [233]
Path: /Volumes/Sims3/The SIMS(tm) 3 Install.app/Contents/MacOS/tgInstall
Identifier: com.transgaming.tginstall-sims3-sku2
Version: ??? (1.0)
Code Type: X86 (Native)
Parent Process: launchd [181]
and this seems to crop up a couple of times:
Application Specific Information:
*** Terminating app due to uncaught exception 'NSInvalidArgumentException', reason: '*** -[NSCFString replaceOccurrencesOfString:withString

ptions:range:]: nil argument'
I don't know if that helps, I certainly don't know what to do with it..! Tried running it on my boyfriend's Mac, which has the same specs as mine, no problems there.