Continuity: When Nancy is singing "As Long As He Needs Me" her dress continually changes between shots from being over her shoulder to half way down her arm.
Continuity: While the boys are messing around with Oliver's stuff, Dodger and Fagin are in the background talking, and Fagin lifts his hand. In the next shot, a close-up of the two, Fagin's hand is down.
Other: When Oliver is meeting Fagin and his boys, he says, "Is this a laundry then, sir?" You can see Jack Wild (Dodger) mouthing that line on the left side of the screen.