The unsinkability of the Titanic: "the White Star Line never made any substantive claims that the Titanic was unsinkable - and nobody really talked about the ship's unsinkability until after the event"
The band played Nearer, My God, To Thee: The band probably did play on deck as the ship sank, but there's no good evidence that their final song was 'Nearer, My God, To Thee.'
The Heroic Captain Smith: Captain Smith really wasn't that heroic. In fact, his inaction meant that there wasn't a more orderly evacuation.
The Villainous J Bruce Ismay: Ismay, present of the company that built the Titanic, is traditionally portrayed as a villainous businessman who bullied Captain Smith into going faster, and then jumped into the first available lifeboat to save himself. But he probably wasn't that villainous in real life. He actually helped a lot of people into boats.
Forcibly barring third-class passengers from the lifeboats: There was no deliberate attempt to prevent third-class passengers from reaching lifeboats. However, "Gates did exist which barred the third class passengers from the other passengers. But this was not in anticipation of a shipwreck but in compliance with US immigration laws and the feared spread of infectious diseases." As a result, only one-third of steerage passengers survived.