http://www.richw.org/dualcit/faq.html

Most of the laws forbidding dual citizenship were struck down in 1967 by the US Supreme Court. The court's decision in this case, Afroyim v. Rusk, as well as a second case in 1980, Vance v. Terrazas, eventually made its way explicitly into the statute books in 1986; up till that time, the old laws were still on the books, but the State Department was effectively under court order to ignore them.

#6
I've heard that the US has a special agreement with Israel permitting people to be dual US/Israeli citizens. Is this true?

No. It just happens that Israeli citizenship law does not require renunciation of one's old citizenship in order to become a citizen of Israel.

In this regard, Israel is really treated no differently than Canada, the UK, France, or other countries which permit people to become citizens without giving up their old status.

It is interesting to note that Israel's "Law of Return" (under which any Jew may immigrate to and become a citizen of Israel) confers Israeli citizenship automatically, without the immigrant having to apply for it, attend any ceremony, or swear any oath of allegiance. The Israeli law may originally have been written this way to encourage American Jews to move to Israel; they could, in theory, argue that they had not explicitly requested Israeli citizenship and were thus still entitled to keep their US citizenship. (Note that Mr. Afroyim, subject of Afroyim v. Rusk, was alleged to have lost his US citizenship, not because he had become an Israeli citizen, but because he had voted in an Israeli election.)

#7
But doesn't serving in a foreign army result in automatic loss of US citizenship?

No. As explained above, essentially nothing causes automatic loss of US citizenship any more. If you join a foreign army, you can lose your US citizenship if you acted with the intent of giving it up. Otherwise, you can still keep it.

Current US law says that foreign military service will result in loss of US citizenship if the person served as an officer (commissioned or non-commissioned) or the foreign military force is engaged in hostilities against the US; the service was voluntary; and (most importantly) the person intended to give up his US citizenship.

Ken Livingstone - Mayor of London on the problems of dual citizenship.

If a young Jewish boy in this country goes and joins the Israeli army, and ends up killing many Palestinians in operations and can come back, that is wholly legitimate. But for a young Muslim boy in this country, who might think: I want to defend my Palestinian brothers and sisters and gets involved, he is branded as a terrorist. And I think it is this that has infected the attitude about how we deal with these problems.