When Bonnie receives a rejection letter from Columbia Pictures, it addresses her as "Ms. Bonnie Parker". The use of "Ms." did not become common until the 1960s. A formal letter of that period would refer to her as "Miss".
When Bonnie sneaks the gun into the jailhouse, a fellow prisoner warns Clyde that he will get sent to the federal penitentiary for taking it. However, United States federal laws in the 1930s did not criminalize gun possession by a prisoner, threatening a law officer, breaking out of prison, or even armed robbery and murder; these sorts of crimes were considered to be solely within the scope of state law. Most federal crimes concerned interstate commerce, transportation, or taxation. (Notably, the only federal crime Clyde was ever seriously accused of committing was transporting stolen autos across state lines.)
When Bonnie and Clyde visit the speakeasy, the instruments heard in the soundtrack (piano, cowbell, large horn section with trumpets) do not match the instruments being used by the actors (fiddle, banjo, upright bass, saxophone, and slide guitar).
As police pursue Clyde and Buck after they steal the safe, officers are seen firing their service revolvers using a 2-handed hold. This technique did not become commonplace until after World War II; around 1930, most pistol shooters would have considered one-handed shooting to be the proper technique.