For now, you can't withdraw BTC from MtGox. You can "buy" them at ~$350 but you can't transfer them to another exchange to sell them, nor transfer them to a private wallet to keep them safe.

MtGox promises that they will soon make possible to transfer the BCT again. Some people believe that the problem will be fixed soon. Some people believe that it will implode and disappear because all the technical problems and you never will see again any of the BTC you "have" in MtGox.

A 50% discount can be interpreted as "the market" believes that there is only a 50% chance that you will see the BCT at MtGox again. (It's really more complicated, perhaps it's a 40% that you will see them soon and a 20% that you will see them in a year. Don't interpret the number too literally.)

That's probably the reason for the discount but I don't think it's a very good one. Suppose that MtGox has all its users' dollars but only half the BTC. Are the BTC holders going to accept a haircut of 50%? No, they'll demand that the pain be shared equally. Even if that argument gets rejected in court it'll still freeze all the dollar assets for a long time. Point is, goxBTC are devalued relative to actual BTC, but goxUSD ought to be devalued as well.

I think the reason goxUSD is not as devalued is because courts can be counted on to recognize USD claims, whereas it's a bit up in the air what Japanese courts will think of Bitcoin. As a result, goxUSD retains more of its value.

No, definitely not this. Japan has good case law regarding the protection of virtual goods, whereas there is a lot of ambiguity on this side of the pacific. If anything this is one point in favor of mtgox being in Japan.

Question from someone who doesn't know much about this: is it possible to know that there is a genuine market in these MtGox bitcoins i.e. that $350 is a genuine market price and not just something made up by the exchange to conceal a complete collapse in value?

It doesn't really matter, except for people that think it is a good idea to transfer assets into MtGox.

(Because fraudulent trades hiding that they can't cover their accounts aren't much worse than the situation where they can't cover their accounts)

I suppose Gox could be buying up all the goxcoins less than $300. But then you'd see a decrease in future volume until the volume reaches zero. They wouldn't do that, because they're not smart enough to pull it off without anyone noticing.

So if hypothetically Gox was the only buyer for bitcoins trapped in Gox, would they be buying them with real USD, or with 'trapped in Gox' USD that may or may not turn out to have any value?

Not being able to transfer BTC out of MtGox