There are so many dynamics to this that it's hard to assess the issue accurately. At first I thought "Wow, this is terrible" but after some research, I'm not so sure.
The way in which they are harvesting the whales is unacceptable.. there's no question about that. Sometimes they die instantly, but other times they can struggle for minutes and up to hours before death. That is in no way humane. Nor is the fact that many whales are endangered. It's also rather shady that they hide their whaling behind a scientific guise. They are not researching and everyone knows it. Even if they are researching, they are researching to see if the populations are able to sustain regular whaling again.
Having said that, what many people don't understand is that whale used to be a major staple in the Japanese diet and has become culturally important. Coming from a rich land like the United States, it's hard to imagine a land where it's difficult to farm to support the populace, but Japan is one of those places. Farming is difficult and whaling has been a great portion of the Japanese food pyramid since about 6,000 BC, or so one early whaling spear suggests.
Another issue worth examining is how humans typically have a problem with killing intelligent or "cute" animals, but cows and chickens get slaughtered by the thousands in this country every day and only hardcore animal rights activists have a problem with it. There are differences, I'm not denying that. Cows, chickens and pigs are raised to be killed for food and whales are not, but we fish don't we? We take fish and crab and lobster from the oceans and they're not raised to be eaten. Also, cows, chickens and pigs are typically killed humanely, but what about crabs and lobsters? They suffer terrible deaths before they are eaten.. they are boiled alive and do not stop feeling pain until their nervous system is literally destroyed, which is just before death, or so most experts say.
If it's done humanely and populations are able to sustain, I don't have a problem with it, but that's not reality at this point. People like those aboard the Sea Shepherd aren't helping.
What is the solution? I don't know. I doubt there will be one. I'm willing to compromise though and I would like to see a non-violent truce in this situation. Issac Asimov once said that violence is the last refuge of the ignorant, and that applies to both sides here. The whalers need to understand that the way and reasons they are harvesting whales for need to change and the world needs to realize these people aren't blood thirsty savages that enjoy making whales suffer.