Although Alan Parker noted that American actors were cast for many of the speaking roles to insure the use of American accents, he pointed out a Cockney accented "Me, too!" as Bugsy rallies the soup line boys during the "Down and Out" chorus.
Moments before Blousey Brown comes to Fat Sam's place for her audition, we see Tallulah kiss Bugsy in the center of his forehead and leave a lipstick mark. A few moments later, however, the mark is much further over to the left hand side of his forehead.
During "Bad Guys", when all of the boys sing "We made the big time, malicious and mad" and take off their hats, Knuckles and Ritzy have messed-up hair. In the very next shot, their hair is neatly slicked back.
When Blousey returns for the second time to Fat Sam's for an audition, Knuckles opens the door. He tells Blousey, "He's busy lady. Come tomorrow" in an English accent. Throughout the movie, he has an American accent.