Obviously, dual citizenship isn't an barrier. After all, the dictator of East Buttfrackistan could declare that all Americans are also East Buttfrackistanis, and, bingo, we all technically have "dual citizenship" (and, if that interpretation were correct, nobody would be eligibile for the Presidency).
So we can rule that list item out in any search for potential flaws in the author's reasoning.
That is a ridiculously false argument. The Law of Nations prohibits such a scenario by limiting recognition of citizenship to circumstances in which jus sanguinnis and/or jus soli exist in fact.
No person who is born with an allegiance to a foreign sovereign may serve as Commader-in-Chief and President of the United States. Barack Hussein Obama Jr. has publicly acknowledged he was born with an allegiance to the Sovereign of the United Kingdom of Great Britain. The Founding Fathers explicitly excluded such a person from being eligible to serve as Commader-in-Chief and President of the United States when they debated the inclusion of the natural born citizen phrase in the Constitution. Until an Amendment to the Constitution lawfully changes the intent of the Founding Fathers to exclude persons with allegiance to a foreign sovereign by removing the natural born citizen phrase used to implement the exclusion, no person may lawfully serve as Commander-in-Chief or President of the United States who was born with allegiance to a foreign sovereign.