That depends on how far out of diapers, and on exactly how much you are exaggerating. A 3 year old could throw a fairly HUGE temper tantrum--for that matter a 4 year old could too but the 3 year old would be more likely IME. And while my kids usually quiet down within 30 minutes or so, my friend told me her daughter's tantrums regularly last an hour or more. And I can recall some fairly baroque crying jags from my own childhood.
I do recall one instance where Owen and I had a very long, drawn out, dramatic argument over his decision to not wear pants (surprise) to bed (pre-potty training). After two hours, it ended with Owen wearing himself out with crying, asleep on the ottoman (naked, of course) and me sweaty and weeping on the sofa. It was boiling hot out, all the house windows were open and I'm slightly surprised the neighbors didn't call the cops, thinking a child was being beaten.
This memory actually nauseats me.
But on the other hand, Matt, if it goes on for a very long time and is accompanied by adult screaming and loud thumping, it might be worth a call to the landlord. If the child doesn't have some sort of developmental issue, it might still be a good idea for someone to check on them.