The issue of killing mammoths with (unpoisoned) blowgun needles, mentioned in the previous thread, is very unlikely to come up for two reasons:
1) There are no mammoth minions.
2) PCs don't use unpoisoned blowgun needles. They're PCs, they use the biggest, baddest weapons available.
The worst case scenario is a dagger-armed rogue killing a cyclops minion (cyclops are large). This does stretch credibility a bit, but no more than D&D always has imo. In prior editions a cyclops on 1 hit point couldn't have been seriously wounded by the attacks that brought him to 1, as his fighting ability, movement and so forth are completely unimpaired. Thus in D&D, people have always been able to kill a (practically) uninjured mammoth with a dart.
I feel the interpretation of hit points that makes most sense, which I'll still be using in 4e, is that until the killing blow, all wounds are minor - shallow cuts, scrapes, flesh wounds. Their recovery via warlord and second wind is explained as a burst of energy - morale, adrenaline - which negates the effect of the wound, though physically it still exists. During a short rest these wounds are assumed to be bandaged and thus effectively healed.
The two alternative approaches have worse problems in my view. Regarding hit point damage as completely non-physical doesn't explain how poison could work or why bigger weapons do more damage. The second alternative, which sees non-fatal wounds such as a blow which takes a 100hp character to 20hp as still being serious, doesn't explain how the wounded character's fighting capability isn't affected.