In my experience, Japan-bashing comes from 4 main sources which I will detail:
China: Self-explanatory really. Until very recently, China was a very stagnant economy and even more stagnant society (in terms of civil and human rights). Since the reality of the present is so bad, let's dwell on the past. As a casual observer of internet forums, you will no doubt encounter Chinese people on there. A common link between Chinese internet users is that they always talk about the past. Most common topics include Mother China's glorious thousand years old history and the many stuff China invented back then. Not now... BACK THEN.
It's not all good in China's past of course and these are conveniently ignored or apologized for. Whether it's the Tiananmen Square Massacres, Mao Zedong's Cultural Revolution (which led to a near-unprecedented amount of deaths) or the many bloody and violent civil wars, to the Chinese mind, these are best not talked about. Let's focus on the good only and shut the mouths of people who talk the bad.
With one exception.
But there IS one thing that unites Chinese people (mainly mainlanders and mainlanders living in foreign countries): Their hatred of Japan in the past, Japan in the present and likely, Japan in the future. Just slip in the word Japan to any conversation and Chinese people everywhere will climb over themselves to remind you of Japan's WW2 atrocities in China and how they should grovel, apologize and plead for forgiveness.
Somehow I don't think an official apology will please them so easily and so fast so I think you'll hear about Japan's bad deeds for a long time yet.
America: To be more precise, I'm talking about the sons, daughters, friends and family of the World War 2 veterans and society, in general.
As we all know, Japan did a few things too to America, the Pearl Harbor attacks being the most well known one.
While the veterans more or less, have accepted the past and look to the future where America and Japan have good diplomatic relations, other people are continuing the hate on Japan. These people still view Japan as the violent and barbaric baby-stabbing imperialist nation instead of the mainly moderate society that it is today.
Which is quite ironic seeing that it is now America who have transformed into the imperialist that they were trying to fight back in WW2.
Why they continue the fight against Japan is beyond me right now, but in the current times, it is clear which of the two nations is the bigger terrorist (I'm ignoring the Hiroshima/Nagasaki and the subsequent fire-bombings for now, a direct and calculated attack on innocent Japanese civilians instead of doing the "right" thing and bombing a military target).
Australia: Yep, that little country down under has a little bit of hate for Japan since they were involved with fighting against Japan too.
The way of hate against Japan is similar to America, they are continuing the fight and taking over the WW2 veterans. And again, the Japan they supposedly hate is no longer the Japan that Japan currently is.
What I would like to talk about is how they communicate their hatred against Japan without appearing xenophobic or the like. They do this via the whaling issue.
Truth be told, nobody really cares that much about the whales. It's just another example of fake sympathy so common in the media and in society. So what does this have to do with Japan? Simple: The anti-whaling crowd are criticizing and hating on Japan, using the whaling issue as the proxy.
Never mind the fact that Japan is whaling LEGALLY, otherwise the nation would have been completely sued by now. But hey, why let facts get in the way of Japan-bashing?
The Anti-anime (and other Japanese things) Crowd: What's this you ask? As we all know, in terms of popular culture, Japan is very popular these days. Whether we're talking about anime, manga (comic books), Japanese-pop songs, Japanese girls, Japanese cell phones, Japanese cars, Japanese movies... the list goes on. If we're talking about the "cool" market, Japan has got it covered.
Of course, like anything else, if something becomes popular, then there will also be a growing anti-crowd. These people usually don't have any logical reason for hating Japan, they just hate Japan because everyone else likes it and it became popular.
Additionally, this anti-feeling can also be explained by nationalism, the simple "local = good, foreign = bad and evil" way of thinking. The fact that many Japanese stuff is objectively better than the local variant renders this way of thinking even more obselete and silly.
Depending on the forum, you'd be forgiven if you thought the anti-Japanese-stuff crowd was the majority. I'd simply equate them as a vocal minority with deeper insecurity problems.