These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Designated Hero: The film treats Dave, Ellen and Duane as heroes despite - or because of - the fact that by not denouncing the substitution they subvert democracy and the US Constitution, effectively depriving the entire US population of the government they voted for.
Fridge Logic: At the end of the movie, the recently-widowed First Lady starts up a romantic relationship with Dave, a man who looks a lot like her deceased husband, and can't account for his whereabouts over the past few months. You think that might make people a teeny bit suspicious?
Eh, people will assume she's also an impersonator.
They might also assume it's something to do with her grief over the death of her 'beloved' husband; a bit unusual, perhaps, but not outside the realm of possibility.
Memetic Mutation: "I once caught a fish this big!" and "we're walking, we're walking".
Protagonist-Centered Morality: When the White House Chief of Staff and Communications Director conspire to replace the incapacitated president with an impersonator in order to pursue their own agendas it is a nefarious conspiracy. When the impersonator himself, his new squeeze the First Lady and a Secret Service agent do the same thing it is portrayed as heartwarming and principled. It kind of helps, however, that the Chief of Staff is doing so for venal and self-centred reasons (in addition to his own corruption, he's basically trying to manipulate the situation so that he ends up as President) while Dave and his friends are doing so with selfless motives and to make the world a better place.
Strawman Has a Point: Alexander objects to Dave beginning to act like an actual president, saying, "Was he on the Trilateral Commission? Was he a senator? Was he in Who's Who in Washington nine years in a row?" Granted, Alexander is totally corrupt and Dave certainly shouldn't be following his orders, but he does have a point that Dave is probably unqualified to be president himself.
Alternatively, the point of the movie is that all you need to be a good president is compassion and common sensenote Things that are mainly denied to a major political figure due to the nature of the office, and the promises and deals necessary to get there. In other words, Dave is the perfect president because he didn't have to do anything to get there.