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 American people of the government they voted for. (Then again, considering a not insignificant number of the other members of the legitimate government were indicted...)
Memetic Mutation: "I once caught a fish this big!" and "we're walking, we're walking".
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.
Even so, Dave is a great deal more qualified than the former President Mitchell because he calls in experts to help him do his job. The only reason he's able to find the money in the Federal Budget is he actually listens to his advisers while making his demands to find and cut unnecessary programs clear. Mitchell was implied to not care enough/desired to keep his hands on the reins of power no matter what.
The FX Series
Unintentionally Unsympathetic: While the show has received generally positive reviews, the Dave character has not been well-received. Dave treats each of the other main characters poorly at least once but does not face any real repercussions aside from Ally dumping him at her sister's wedding. The other characters have been well received, however.