I have found resetting my SRam is a good workaround for the many errors I get when trying to launch the game. This occurs with or without mods. The process only works once. Is there a more permanent solution, or do I really have to shut down & reset every time?
Game Information:
Sims 3 version 1.67.2.024001
Late Night Installed
High End Loft Stuff Installed
All new in shrink-wrap

System Information:
Mac version 10.10.5 (Yosemite), originally running Snow Leopard
Processor: Intel Core 2 Duo
Graphics: NVIDIA GeForce 320M 256 MB
RAM: 2 GB 1067 MHz DDR3
Memory: 43.96 GB available after install
VRAM (Total): 256 MB

Error List (in order of frequency):
Disk Authentication Error: "Disc Authorization Failure. We are unable to verify that your disc is a valid copy of The Sims 3. Please contact customer support."*
* When the Career mods are installed, the error message may appear in front or behind the mod message.
Game Process Failed, followed by two more windows opening and the game process starting > Disk Authentication Error
Game Process Failed > Crash
Disk Authentication Error > Crash

Although TS3 for Mac can only utilize 2 GB of RAM itself thanks to the kooky way EA did its implementation into OS X, your Mac only has 2 GB total? That's really tight. It could certainly benefit from having more to work with overall if possible. Also, most who play the Mac version have to (sudo) purge RAM using a Terminal command before and frequently during play to keep things under the limit. It's essentially a best practice now.
https://bluebellflora.com/resetting-ram-during-gameplay

Yes, the computer is very old. I should see about getting more RAM for things.

Thanks for the tip!

Not everyone can realistically afford to do that.

For all of the flaws that TS3 for Mac carries with it, one thing that works in Macs' favor is that they can make better use of subpar graphics cards and even underpowered CPUs when necessary due to the better optimization of OS X and the way in which the hardware and software all fit together as if they were made for each other (which they are). That's why, though I would never recommend this, so many players on ~1.4 GHz MacBook Airs can get the game with the earlier EPs going whereas lighter weight PCs with similar specs on Win 7 or higher would mostly likely choke during the game's startup.

I'm almost positive that last part your purchasing advice was meant to be humorous. But coming from someone who chooses to be surrounded by products from both universes, sorry, I have to say it was totally inappropriate and not helpful. If the limitations of TS3 for Mac are too much for the player to bear on OS X, they can bootcamp Windows (as many players including me have done) and play on the Windows partition. Not on the OP's system, I do agree its age and weak processor are working against it, I mean on a stronger one. But for other purposes, OS X is where some of us choose to be on our own time and we do not deserve abuse for that.

The reasons I am willing to pay more for an iMac for my personal use than another desktop with similar specs are the pleasantness of working with OS X and they just plain last longer. At least, that has been my experience. Others have varied. Please do not confuse sensitivity or loss of objectivity with just plain being annoyed by 1990s style product line bashing. For what it's worth, not everyone here is going to instantly recognize that you do mean to be helpful with such advice, given how much time you spend helping others with various issues and venturing into downright innovative solutions on this site.

You do have a point about the GPU in this case, but the player only has one EP and it's not a particularly graphics heavy one. The game ought to run better for them than it does in their current environment, except that with Yosemite as their current operating system there just isn't going to be enough RAM to go around. I ran Mavericks, that system's predecessor briefly on an older MacBook Pro with only 2 GB in an effort to fix something else about it (which turned out to be a waste of time as that one was just too old to keep running, really) and although it did work and was stable, it was sluggish for routine tasks and there sure wasn't much RAM left to work with. This wasn't sims related, TS3 would have been totally out of the question there.

Your points might have more credibility if you didn't have to exaggerate while making them. Apple products are not and were never double the price for equivalent specs and build quality. Besides that, PC users are ugly, their mothers dress them funny, and for some reason they all have viruses. (As you can see, I'm not very good at this kind of discussion.)

Sorry, I don't think we meant to wander quite so far away from the OP's issues here though.