Good grief, Fagin. FAGIN. How do we properly trope him? He's cast in this adaption in a much lighter and comedical tone. But the lovable rogue's character bounces all over the place. One minute he's fun and endearing, the next mentally unhinged, if anyone stumbles upon his secret horde. He gives the orphaned children of London a home, and teaches them how to survive, whereas the alternative is begging on the streets or ending up in the Workhouse. But despite the wealth he's accumulated, doesn't do much to improve theirs (or indeed his own) squalid living conditions.
Sikes can sometimes come under this too, particularly in his relationship with Nancy. It can be played as pretty much everything from him truly loving her and killing her more out of grief that she's betrayed him than outright anger, to being fairly disinterested in her and tolerating her presence for as long as she worships him.
The song "I Shall Scream". While it can be pretty funny, it has absolutely no bearing on the plot. Rather fittingly, it's left out of the 1968 movie version.
It establishes a romance between Mr. Bumble and Ms. Corney, which is referenced later during one scene in the second act, and is thematically important: the Bumbles are evil, selfish people, and thus they make each other miserable rather than happy.
Cleverly subverted with "Oom Pah Pah". Upon first viewing, it's just a merry drinking song to get everyone in a good mood and doesn't appear to have any bearing on the plot. Then Sikes comes in...
One-Scene Wonder: Noah Claypool only gets one scene, as opposed to his long and loathsome presence in the book. However, he avoids being Demoted to Extra via making quite an impression during his brief time on stage.
Twice he gets in big trouble because he just stands there like a deer in headlights - first when Dodger and Charlie pick Mr. Brownlow's pocket, then later when he accidentally knocks something over in a house he's trying to rob and he just stands there until the lights come on upstairs.
Arguably Fagin and Dodger suffer this as well when they allow Oliver to "go to work" when he's been with them less than 24 hours and is clearly still far too honest and naive to be ready to pick pockets. (This is mainly due to Adaptation Distillation since in the book, Fagin forbids him from going out for several weeks while he's being trained).