MtGox, however is a real company and operates under Japanese law and international trade agreements. The company is still liable to the customer in more ways than they'd like to be, even if tries to set its own rules -- the law always takes priority. Your analogy is not quite the same, because bitcoin are a lot more traceable than that.
Yes, but if at the end of their investigation, they are unable to ascertain that you are owed funds (which is what it sounds like they are saying) then that's all they have to do internally (assuming japanese law is similar to us law--i claim to be an expert in neither, but I have taken quite a few law classes and had some experience in the field). Your choices are to sue them in court, where you will have the burden of proof that the money is yours AND that MtGOX was negligent in crediting the money to someone else's account. The first is going to be hard to do, the second IMHO is going to be impossible. YOU made a mistake that resulted in a LOSS for YOU. Depending on how long ago this happened, you may have a claim if you can figure out who the account holder of the other address is. In most places, after you find something of value not to be yours, you are required to make a reasonable effort to locate it's owner. (In most places this is done either by filing a police report or taking out an ad in the local paper though courts have ruled other methods to satisfy this requirement). If after a certain period of time no one has stepped forward to claim the item, it becomes yours (it was abandoned).
THIS is what MtGOX is telling you to do in regards to the police report. You misplaced something and by filing a report, you may be able to claim this item later if it shows up in another police department's system or some other database. Once again, you will have to prove that the BTC actually belong to you (kind of like identifying a ring when you go to pick up a found item). Will your local detectives put in a lot of work into finding something that amounts to $700? Probably not, but it'll be your best shot. Think of it as the equivalent of filing a report saying I left my ring on the top of my car in WalMart's parking lot and drove off and now I can't find it.
Can BitCoin stay unregulated for much longer? Since it seems that somebody has already figured out to artificially scatter transactions so that they are effectively untraceable, the are many ways to launder money with this.
Irrelevant: it only matters if it is regulated AT THE TIME of the issue arising.