Before this, Disney had never touched modern-day New York City as the setting of an entire animated feature. (The beginning and end of The Rescuers take place there, but most of the film is set in Louisiana.) Not only did they pull it off, but then the second musical number "Why Should I Worry" starts up, and the audience realizes this is going to rock.
Upon first meeting Sykes, his dogs, Roscoe and DeSoto, go into the gang's hideout and starts terrorizing the place. DeSoto finds Oliver's hiding spot, and ignores Roscoe telling him that Sykes is calling them back, in favor of preparing to eat Oliver. Oliver responds by clawing DeSoto's nose in self-defense, leaving scars. Even Fagin says that that took a lot of guts.
After the clawing mentioned above, the two pinchers, naturally, get angry and are about to kill Oliver when the rest of the gang suddenly leaps to his rescue! And this is the same gang that hated him just minutes before! Also doubles as a Crowning Moment of Heartwarming.
Fagin coming to save Jenny and his pets, on his scooter. When you saw all through the movie how scared he was of Sykes, this definitely proves how brave he can be.
Seeing Jenny in danger, Oliver jumps into the back of Sykes' limo during a frenzied car chase. He ignores the fact that Roscoe and DeSoto are in full-on attack mode and bites Sykes on the hand.
Dodger somehow saves Oliver's life after the car that they were in gets knocked off of a bridge in flames.
For Tito, driving the scooter off the railway just before they hit the train. The way he does it is pretty funny too.
Fagin, upon seeing Jenny sad and worried about Oliver, willingly gives him back to her (after pretending to mysteriously find him abandoned in a crate) despite the fact that he knows that Sykes will kill him if he couldn't get the ransom money.
Dodger and his gang ultimately redeem themselves for their friend Oliver by helping him and Fagin rescue Jenny from Sykes. Bonus points for Georgette helping as well.
Bonus points also for Dodger, who had earlier all but called Oliver a sell-out for wanting to stay with Jenny, being the one to declare that they'll save her.
It's a small moment, but after Rosco and DeSoto fight and wound Dodger on Sykes' command, Fagin, who had spent the entire film terrified of Sykes, reaches down to comfort Dodger and gives Sykes a Death Glare.
Dodger jumping in to defend Fagin from Roscoe and DeSoto. If you look closely you can see Dodger actually overpowering DeSoto despite the latter being much bigger and more vicious than him. He only loses the fight because Roscoe jumped into the fray.
Despite being pretty brutally mauled by the two dobermans, Dodger seems pretty nonchalant about it when Rita shows worry.
Francis: (to Roscoe) Isn't it rather dangerous to use one's entire vocabulary in a single sentence?
Tito: Aha! Frankie, you did right! (gives him a high paw) You bad, boy!