So, I only had one controllable family in an apartment. All other 3 slots were available. I recently moved in two new couples in individual apartments (which makes it a total of three). When I tried playing the first family, it's like the other two families never moved in. As in, they are unable to visit them as their door signals "Vacant" (or is inhabited by some random townie). But the other two families don't have that problem. What's the cause of that?

Did you click on the apartment door and select "Rent"? They need to do that before other apartment residents can see and visit them.

Yeah I did, I even furnished their apartments and played with them a little. The two newly-moved in families do not have this problem, they can see everyone else just fine.

I've had that a few times. Sometimes the game is just mean. I'm not sure how to fix it though...

Try using the Batbox (AKA FFS Lot Debugger) to fix the issue. Look for the "Fix.../Bad Apartment Residencies" option. Be sure to back up your game before using it!

Well, that didn't work sadly.
Stupid bugs...