I was getting error 13 non-stop, but managed to (so far) get rid of it. It wasn't due to saving infrequently (I saved every 2-5 minutes, a habit from the frequent TS2 crashes), and I had no success with deleting cache files, .BAD files, or changing a tree or other random action on a community lot. I also tried renaming my game, using backup files, and moving my active family to another lot. I didn't have an excessive amount of downloads or mods installed, nor much of a population, and I play with a legal copy. However, for over a month and a half, I was able to save only one time per game, and then never again.

This error may have occurred only after I significantly re-built a lot I had downloaded off of MTS. I was trying to expand the family's house, and had deleted most of the house they had been residing in, in order to rebuild on the same plot with their garden. I believe this is when error 13 began, but I can't be sure.

So yesterday, I used the TS3 Launcher and uninstalled every custom lot I had in the game (I kept all my hacks and other .package files, however), then started the game, saved my sim families to the library, as well as three community lots I built myself, and deleted the entire neighborhood. I began a new Riverside neighborhood, and built a brand new house on an empty lot. Then I played until 8 AM in the morning (only about ten hours straight), saving every 2-5 minutes, and not a single error occurred. I have not placed any of those custom community lots I'd built as of yet, but will try that out after a few more days of finally enjoying the game again.

I hope this helps someone out, as there seems to be a lot of suggestions out there, but barely any follow-ups on their implementation.