Wondering if there's a fix for some old issues

Not sure how long you have been away or if you averse to using mods, but Shimrod has a Dive Cave fix mod available at The Sims Asylum that he produced in 2013, soon after IP was released. I could link to it, but there would be nothing to see unless one is logged in over there. He's listed under Retired Creators. The mod's description page should tell you if it fixes the particular glitch you are remembering. As he notes, usage of NRaas DebugEnabler is required for his fix to work.

Not familiar offhand with the Medusa statue issue, can you expand on that a bit?

As for other issues, sure but there would be far too many to list. We kind of have to take individual game glitches (as opposed to the Nothing is Working Well kinds of problems) on a case by case basis.
http://www.nraas.net/community/TIPS-FOR-BETTER-GAME-PERFORMANCE

There have been no fixes coming from EA for TS3 as the game has been out of development for over five years now.

I'm not adverse to mods, as I've recently started using them in Sims 4 and I remember a few back in Sims 1/2. However, I'll need to learn how to use them for Sims 3 as I think the process for adding them is a bit different?

The statue issue is when you send your Sims to the junkyard to find furniture, and sometimes you find a Medusa victim statue. You have your Sim collect it, but instead of going where the rest of the items go, it goes into your personal inventory and gets stuck, you can't get it out.

Thank you, I'll check it out :)

TS3 mods are package based content and require the Framework to be inserted into the player's TS3 user game folder in Documents in order to work. It's really just three folders nested correctly and the one require Resource.cfg file. The mods, or other forms of package based content, go into Mods\Packages once unzipped.

This version of the Framework is downloadable in its entirety and comes with two small sample script mods that can be used for testing and then kept or removed as desired.
http://modthesims.info/wiki.php?title=Game_Help:Installing_Sims_3_Package_Files/Setup_and_Files