Which state of the United States is farthest east?
If you consider “east” as starting at the 180th meridian, it’s Alaska instead of Maine.
This Englishman formulated the theory of evolution by natural selection after extensive travels among tropical islands.
Who succeeded Grover Cleveland as President?
Who are three people who have never been in my kitchen?
Who was the 1st President of the United States?
Archibald Campbell, Chief of that Ilk and Earl of Argyll, was the son of another Archibald Campbell and the grandson of William Douglas, Earl of Morton. He was de facto ruler of Scotland for a while, and for a while was an important supporter of King Charles II, but, charged by that King with treason, he was eventually beheaded on ‘the Maiden’ at Edinburgh for treason against his King, with both head and body laid to rest in Kilmun Parish Church. He was succeeded by his son Archibald to whom his lands were eventually restored. In what year did his beheading by ‘the Maiden’ occur?
Among the world’s 30 most populous cities, which has a name that translates to ‘City of Angels’?
This doesn’t quite satisfy the OP, because both answers are wrong.
Despite what some Internet would-be pedants will tell you, the only correct answer to that question is George Washington. If you’re going to argue that Peyton Randolph was “President of the United States”, then you’d have to likewise say that the current President of the United States is Mike Pence.
3 correct answers here?
Sucre, La Paz, and “B”.
I’ve heard this one a lot, but it includes one questionable line. Did Teddy ever run for a third term as President? As Vice President he replaced the assassinated McKinley and ran for President in 1904. Were those therefore two terms? Not by modern usage. Roosevelt was the first VP turned President to run for re-election, though. Some people at the time did consider the period from September 1901 to March 1905 as a term but only a very few. I don’t find any hits on Google Books from 1912, when Roosevelt actually did run as a candidate, for that use applied to him, although some exist from 1906.
I think junking that line improves it.
Who’s the first President of the United States, in contrast, has only one answer. Any fudging on it is historically wrong.
It orbits the Sun and was called a planet when discovered, but was ‘demoted’ when similar bodies were discovered, and is now called a dwarf planet. What is its name?
And the boliviano. That’s a favorite gimmick of crossword editors.
Excellent.
I’m not sure this satisfies the OP, because it is impossible for there to be exactly two correct answers. There’s either a unique answer or at least four correct answers.
I think the trick here is to ask the question before the wavefunction collapses.
LOL, maybe. But the OP was not “exactly” it was “amazingly” 
Also, there are 3 answers to who ran for governor. The recently departed Sonny Landham unsuccessfully ran in Kentucky.
I like mine better, because otherwise you have to count Punjab. Or all the Springfields.
This might be slight hijack, but it’s surprising how often I have to give complex answers to simple English questions.
“Is there a word for fear of heights in English?”
“Yes acrophobia. But no one will understand that. People use vertigo…but it’s not correct. You know what…just use * fear of heights *”
I guess the OP didn’t consider a case like your kitchen, where the existence of only one correct answer would exceed the existence of two or more correct answers in amazingness.