Factual error: Warren Beatty refers to the "Hoover Dam" being able to generate the power needed for Las Vegas and his Flamingo casino. The problem is that he supposedly made the comment in 1937. At that time, the "Hoover Dam" was still called "Boulder Dam." It wasn't renamed to honour President Herbert Hoover until about ten years later.
Continuity mistake: In the kitchen scene where Bugsy has made a birthday cake for his daughter but has missed her party because guests arrived, the camera shot changes from Bugsy to his wife and back a couple of times. When the shot is from behind Bugsy, there is smoke coming from the birthday cake candles. When from behind his wife, there is no smoke.