My sim's goal is to be a chess grand master but he can't do that if he can't work his way up the challenge tower. And yet there's a big invisible wall in the not-form of Carlos Mancini in Monte Vista. He shows up, but he doesn't *show up*. Even when he's interacting with other sims, he can't be clicked on and doesn't show up. I had to engage him in a game of catch to find him, and yet I still can't invite him inside. He doesn't show on the map anywhere--there's no family by his name, and he isn't shown as being home in any house even when I reset him (and since he's interacted with some of my sims, he should show as being at home, right?). So I can't even find him to evict him!

How do I fix this?

That one has an interesting backstory: http://sims.wikia.com/wiki/Carlo_Mancini

But anyway, if you are using NRaas mods here are some things to try.

DebugEnabler: On City Hall, Fix Invisible Sims.
MasterController: Try using MC's Focus command run from City Hall on him (not immediately after being reset, then he won't show up anywhere until the game clock runs for at least a few sim minutes). If you can find which lot he is on, click on the ground or wall of a building on it and force change his outfit. The invisible sim thing can happen when sims' outfit assignments goes bad.

A variety of ways: Temporarily make him/his household active, you don't have to save afterwards, just to see what's going on with this one and where he lives.

What if I'm not using NRaas? And I don't know what house he's in so I can't make him active.

What purpose are the backstories supposed to serve, anyway? It isn't as though they show up in the games.

It's going to be very difficult if not impossible to fix this without MasterController. Do you have story progression on while you play? The Manicinis live in the house next to the library in the walled-in part of town on the top of the hill when you start a game. If that house is empty then story progression must have done something to them, moved them somewhere else or made them homeless.
There's also the possibility that the game has killed him while he was already selected as your next chess opponent but due to him having family still exists as a thumbnail (MiniSim) but not as a full Sim anymore. Have you seen him in game? Does he show in your Sim's relationship panel? How high is your relationship level?

One way to perhaps "fix" this is to travel to another world. The game creates chess opponents there, too, so, if you're lucky and have moved up the challenge ladder in another town the game will have dropped Mancini in your homeworld once you return and give you somebody else.

Oh goodness thank you I was finally able to delete him with that location. I just moved him out and not the rest of his house. Nobody else in his house was named Mancini though! No wonder it was so hard to find him.