about the 'not looking realistic' thing, I had that at first too. until I understood DePalma was much more trying to make a stylish cinematic work instead of a raw, neorealistic gangster picture, true to the facts and everything. It's not that. Ask Omar: DePalma uses a lot of Hitchcock elements.
spoiler warning
The scene with the baby carriage in the train station is an hommage to the famous Odessa stairs scene in "Battleship Potyemkin" by Sergei Eisenstein (silent, black/white film from 1925) and is filmed in Hitchcock style, as well as the scene when Capone's men go to Sean Connery's house