"We have nothing in the house to eat."
Translation:Ni havas nenion en la domo por manĝi.
mi ne havas ion I would understand as "I do not have something"
mi havas nenion as "I do not have anything"
Neither of them are "correcting" (korektaj) (i.e. related to the action of correcting something), but I would say that both are correct (ĝustaj) but with different meanings -- the first of them being a slightly odd thing to say, though. I suppose it means "there exists a certain something which I am thinking of but which I do not possess", i.e. "there's something which I don't have".