Hey don't be so discouraged. The military is not for everybody, but if you are deadset on being military, it can happen. First of all, about the vision thing, I have known guys with 20/100 uncorrected to get waivers to be a pilot. They were told they can't be pilots, but that they could be a navigator, and got a waiver while waiting nav training and then got upgraded.
Also, about the dual citizenship thing. The reason why that is an issue is because as a Pilot/Nav and various other AFSCs, you will need a Top Secret clearance. Foreigners are not privy to a majority of the classified information, so if you are a dual citizen, who is to say that you won't give your knowledge to your second alliance?
Anyhow, the dual citizenship aspect was not as big of a deal pre-9/11. I do know a guy who is a dual citizen and has a Top Secret clearance but he has a unique case. He is a dual citizen of USA and Brazil. When the Air Force told him that he had to renounce his brazilian citizenship, he tried and Brazil said no. So then the State Department called Brazil and Brazil said no. So he was required to cutup his passport in front of a US Citizenship and Immigration Services Officer (USCIS) to prove his loyalties to the US. He still loves Brazil, married a Brazilian girl, and plans on retiring in Brazil. The only problem is that US Citizens are required to acquire a visa before entering Brazil, and he can't get a visa because he's a Brazilian citizen, but he cut up his passport. That's another story in itself. What I'm saying is that you can ask Sweden if they would recognize a renouncement of your citizenship or not. If they don't recognize it, you would retain your Swedish citizenship even though you did everything in your power to renounce it. I don't think it would hurt to ask (and it depends how much you want to be in the military).