Well, I checked the float, and it appears to be okay. The toilet is filling the tank to within a centimeter or so of the fill line. And it dumps the water out of the tank quick enough, I guess. I don't know, I've never really watched a tank empty before this. We replaced the flapper, and it's still having problems.
Well, this has turned into an interesting theoretical problem. . .like I said, the landlord is working on it now.
Thanks for all the advice and input. It's appreciated.