What Should Candidates Know?
Back when she was still running for President, Amy Klobuchar was criticized for not knowing the name of the President of Mexico. That was reminiscent of the criticism of Gary Johnson in 2016 for not knowing what Aleppo was. (On the other hand, Trump seemed to be undamaged, though he was certainly ridiculed for it, by the revelations that he thought that Frederick Douglas was still alive, that we might be able to stop a hurricane with a nuclear bomb, or that we might be able to stop Covid-19 with an ordinary flu vaccine.)
Incidentally, I don't believe the news media who report on things like this have any interest in those facts, except to attack someone for not knowing them. The Gary Johnson story was literally the first and last time I ever heard the word "Aleppo" anywhere other than in a computer game, and pretty much the only fact about Aleppo that they reported was that Gary Johnson didn't know about it. Likewise, the only information I have heard about the current President of Mexico is that Klobuchar didn't know his name.
By these standards, I myself would not be educated enough to serve as President. I think this is a reductio ad absurdum, since I'm also highly confident that I am in the 1% most educated people in the country, maybe the top 0.01%. (On the other hand, I wouldn't have thought of dropping a nuclear bomb on a hurricane, but I guess that doesn't matter.)
This raises the question: what should we expect a presidential candidate to know? What is the sort of thing that, if they don't know it, we should take that as disqualifying, or at least a major strike against their candidacy? I guess I'll assume this is in a possible situation where there are multiple candidates who are decent people, so you're not forced to choose between ignorance and evil.
Arguments for 'the President of Mexico'
Information Needed for the Job
You can see the argument that the U.S. President needs to know who the Mexican President is, since the U.S. President will have to deal with that person, perhaps negotiate trade deals, etc. This is just practically relevant information for doing the job.
Reply: Don't be silly. At the time our President has to meet with the Mexican President, the President's staff will brief him or her on the important facts and background of the meeting. The U.S. government is huge, and it obviously contains top experts on all the major areas of U.S. policy, and all those experts are ready to serve the President. It's not like Klobuchar would go into a meeting with López Obrador and not know who he was.
Sign of General Ignorance
Second argument: "That's all true, but not knowing something like who is the President of Mexico just shows that a candidate is a generally ignorant person, and probably not educated enough or intellectual enough to be a good President."
Reply: Yeah, I think that's silly too. Actually, I think that a person who believes that "second argument" is revealing their own ignorance and naivete. If you knew who the President of Mexico was, congratulations. But that's one of about a million details that someone could say "the President needs to know in order to do the job." It is naive and simplistic to think that a normal person (not someone with a freakishly encyclopedic memory) would carry around all that information and be able to call it up when a random item from the list of "important facts that the President needs to know" is selected to question them about. That is not how this thing works. The way it works is that the President is surrounded by experts on many different things, each of whom knows their own limited area, and the President talks to the relevant people when a decision needs to be made.
"Educated people" do not know all the important facts in the world; no one does. Most educated people know a tiny sliver of the world's important facts, they are shocked that everyone doesn't know the specific sliver of stuff that they know, and they assume all the other stuff outside their area is unimportant. They also typically don't realize just how much stuff that is.
If we keep doing this "gotcha question" tactic, we're going to be selecting for Trivial Pursuit champions. A Presidential candidate's campaign preparation is going to consist in memorizing long lists of details. Start with the names and locations of all the countries in the world. (There are ~200 of them. How many can you name? What, are you unaware of the very existence of dozens of entire countries?!) Then the head of state and form of government of each country. Add in the names and locations of all the major cities in the world that are involved in any important news story that has happened in the last 5 years.
The candidate will have to review all major news stories from the last several years, and will have to memorize all "important" details contained in them. If there is a war somewhere, the candidate will have to know the names of all cities involved in it, the major factions, the cause of the dispute, the leaders' names, when it started, etc. He or she must also know all terminological variants on any important thing in the story. E.g., if there was a disease outbreak, the candidate has to know every alternative term used to refer to that disease, lest a reporter catch him off guard with an unfamiliar expression and force him to ask "what is that?"
There are many more details that could be said to be necessary for the President to know. Surely, if one is going to take the oath to uphold the Constitution (that's the only thing Presidents are sworn to do), one must know the Constitution, right? So a candidate will have to know the name and content of every 'important' Constitutional provision.
They should also know all the major laws and issues in every important area of policy -- farm policy, energy policy, education, labor, health care, highway transportation, pollution, water, immigration, emergency services, tort law, illegal drugs, prescription drugs, health and safety, disaster relief, space exploration, arts, banking, air traffic, firearms, military defense, etc. Those are just a few areas of government policy that I can think of off the top of my head. I'm sure there are many more. You'd have to spend at least several hours studying about each of these things, because some hostile journalist can ask you about any one of them, picking a random technical term from that area. Like, "What do you think of the nuclear triad?"
Or rather, this is what would happen if voters cared about this sort of thing as much as journalists purport to care.
Fair Questions
That said, I don't think all knowledge questions are unfair, and I think some kinds of ignorance are genuinely disqualifying.
Knowledge of One’s Own Policies
The first category I'd suggest is that of key facts about a candidate's own proposals, particularly facts that would be needed to assess whether the proposal is a good idea. Thus, if some candidate proposes to offer Medicare for all Americans, that candidate should know such basic things as how much this would cost and how it could be paid for. It's fair to ask these questions, since the candidate would have to have looked at those things in order to arrive at the conclusion that this is a good proposal. If they didn't, then the candidate is either irrational or campaigning on false pretenses.
General Understanding
I don't think a candidate needs to know specific details such as the current Mexican President's name. But I think a candidate needs to have a general understanding of how many things in the world work. This sort of general, diffuse understanding of our world is not the sort of thing that particular policy-area experts are likely to give the President on an ad hoc basis.
Thus, for example, I think it's worrisome that a President would think that a nuclear bomb might be a good solution to a hurricane. This suggests a kind of confusion that advisors couldn't just straightforwardly remedy by reminding the President of a little factual detail. It suggests a person who probably would not be a good decision-maker, even with experts to feed him all the factual details.
Or, for a different example, I should think it worrisome if a President was under the impression that health care for everyone in the country could be paid for by a tax on billionaires. (If all the country's billionaires gave all their accumulated wealth to the government, it would fund the federal government for nine months.)
Under the heading of general understanding, I would say that a candidate ought to have a basic understanding of economics, of the sort that you'd get in econ 101. Thus, they should not think that price controls work, or that the trade deficit represents a "loss" to the U.S. They should know what a demand curve is, and how the Fed lowers interest rates. I list these things because (a) it's plausible that you have to understand these things in order to make a lot of policy decisions intelligently, and (b) it's unlikely that the President's advisors will successfully remedy a complete ignorance of them on an ad hoc basis, each time the President needs to make one of those decisions.
Attitude to Experts
A leader needs to have enough understanding of how the world works to know when to rely on experts. He should not, e.g., think that he knows better than medical professionals do about the properties of a new disease. This is crucial since no individual knows enough to competently manage all the things the government has its hands in. (This is one reason for thinking the government has too many hands in too many things. But leave that aside for now.)
On the other hand, a President should be able to recognize what sorts of things an expert cannot authoritatively tell one, or what they cannot be trusted to be objective about. E.g., he shouldn't gullibly assume that experts in industry X can be trusted to say what are the best regulations for industry X.
Rationality and Goodness
The final point isn't a matter of knowledge per se. But a good leader needs to be able to weigh the information that advisors give him, and to make a decision based upon rational moral considerations (as opposed, e.g., to making purely self-interested choices or emotional choices). The leader has to care about what is just, what rights people have, and what is good or bad for society. These two key traits -- rationality and morality -- cannot be supplied by advisors (as ordinary factual details can be); the leader has to have these traits as standing features of his character.
So those are the sort of things that questions aimed at political candidates should try to draw out. Journalists shouldn't be trying to find factual details to trip candidates up over. They should be trying to get candidates to display how the candidates think about a normative political question.
This calls for questions of detail about the justifications for policies that the candidate supports. People who are used to thinking seriously about normative questions will be able to address objections. If reasonable, they will be able to recognize valid concerns and reason to a conclusion despite the existence of uncertainty and mixed costs and benefits. People who are not serious about figuring out the right answers will find it hard to fake those things.
Of course, by my standards, most (nearly all?) actual politicians would probably be disqualified.