I don't think that most people find Fnordian's first objection to be much of a problem. I always assumed that although I was rational while I was behind the curtain, once I 'came out' I would be born anew into the world I had created. The tricky bit here is that the Veil of Ignorance is a gedanken experiment, and no one is actually going to go behind it or come out. It's just pretend. First you pretend what it would be like to be born poor. How would you like the world to be? Then crippled. Now how do you want the world to be? Then stupid. The brilliant. Then rich. And eventually you decide which world suits all of these people the best.
Fnordian's second point is much more important. It means that the Veil of Ignorance can only be used to help you find your perfectly just world. Other people will find a different just world.
Then we can either have a Congress of the Ignorants, to duke it out among themselves, or we can use a MetaVeil, behind which you don't even know what your opinions are on matters like the desirable level of basic living conditions and diet, or ethical matters like personal property and basic rights. This might be what Rawls meant by the "conception of good", but I think he didn't mean anything so overwhelming. I don't think that I could do that gedanken experiment very well at all.
One of the reasons that I can't do that experiment is because the factors involved just get too weird. There are those who think animals have rights. Do I have to assume that I might be born as a dog, deer, or fish? Do I have to weigh the just worlds of a shark, a tuna, and a fisherman, and find the happy medium? There are way more cockroaches than humans. Will the 'just world' end up being correspondingly weighted towards the ideals of cockroaches? Or is it only weighted that way within the percentage of people that think that cockroaches have a concept of just to weigh? Should I count the cockroaches themselves as being among those who think that cockroaches should have a vote? Oy vey.
The Veil of Ignorance is great as a jumping off point for finding a just system, but it's more a fun idea than a complete philosophy. And that's the problem.