US President Obama was not elected, either. He was appointed by majority vote of the Electoral College. This is a hair-splitting, technical, de jure distinction, obviously, but denying that it exists is pretending that the republic is more democratic than it is in fact.
An election is a popular vote. A parliamentary or republican representative vote is not an election, regardless of how much it may superficially resemble one.
Except in the U.S., electors are required to vote for the candidate that won the majority of the popular vote in their state. They're honorary officials and rarely have any autonomy, though that is governed by state laws, not national laws.
http://www.archives.gov/federal-register/electoral-college/e...
The facts are still the definition of the word "election" and the contents of the national constitutions. There is no amount of rhetorical gymnastics that you can perform to make "Hitler was elected" anything other than a provably false statement.
It doesn't matter. Clearly, there is no specific requirement that a democratic society has to pick its leadership in free and fair elections, nor do elections prevent jerkasses from becoming dictators.
A critical amount of people voted for the candidates of the NSDAP (33.1% of all votes, the relative majority of the last 1932 election), who in turn formed a coalition, with Hitler als Chancellor. Formally, the president appoints the government and the chancellor, and the party resp. coalition of parties with an absolute majority of seats in parliament is who is normally appointed (and I think there is a certain legal obligation, but I'm not 100% sure on that).
The current German political system is in fact very similar to the one of the Weimar Republic (with details like certain thresholds to prevent dozens of tiny parties). Claiming Hitler was never elected is like claiming Angela Merkel was never elected.