I have never said that it is impossible - only that big lawsuits like this move at a glacial pace when they are dealing with domestic parties and assets - the fact that the company that is being sued here and its assets are in many foreign jurisdictions will only slow this process down further.
So like I originally said, this might not be a huge pressing concern for mtgox as it isn't likely something drastic would happen overnight.
Then we're agreed on that part. Also, the number of lawyers with experience in enforcing judgments internationally is limited. They don't come cheap and if you have to fly them to where you are, they're flying first class.
I also don't believe they're going to get anything like assets frozen before getting a judgment, unless they do something dumb like try to hide them and get caught. No court in its right mind would basically destroy a business based on a breach of contract case the other side might not even win. For one thing, seizing Gox assets would basically instantly destroy the value of the company and render it unable to pay any judgment.
That aside, even if Japan has agreed in certain areas to have the same law as the USA that definitely does not mean an order from an American court will be enforced in Japan. Even if the Japanese court is satisfied that the American court made the correct decision in law it still might decide that America was not the correct forum or that according to their laws the proper jurisdiction was Japan. In that case you'd have wasted tens of thousands and months/years of your time to get a court order that is worthless.
But not this part. Generally, as a matter of international comity, and pursuant to treaties to which both Japan and the United States are party, courts from one country do not act as appeals courts for those of another. So long as the proper procedure is followed, the United States and Japan will enforce a breach of contract judgment from a court in the other country.
Japan, just as the United States, enforces choice of law and choice of forum provisions, and this contract has an unambiguous agreement to jurisdiction and which law applies. Neither a Japanese nor an American court are going to tell the court of another country that they got their own law wrong. I'm not going to say something like this would never happen or that courts never play favorites with a local company, but it's very unlikely in this case.
You might see something like this where one party gets a default judgment against the other, with the other having basically contended there was no jurisdiction the whole time and then collaterally attacking it only when the other side tries to domesticate the default judgment. But you're really not going to see a Japanese court say a U.S. court doesn't understand its own law.
The U.S. and Japan have deep and lasting business relations, and you don't want to sour that by making contracts between companies unenforceable, because people will stop doing business.