Even more so, his brief conference with Lady. It really shows how close they are; they didn't even need to discuss the situation, they play off each other so well. Also, Tramp's tone when he comes bursting onto the scene; he's deadly serious, because he can tell that Lady is deadly serious. There's no time for jokes, and he doesn't make any. For Tramp, that's a big deal.
It's a reminder that Trusty's not just a retired hunting dog—he used to track criminals for a living. His owner is probably a retired policeman or something along those lines. Trusty knows what he's doing, weak sense of smell or none.
Trusty: Why, some of the finest people I ever tracked down were jailbirds!
Going off of that, the absolutely bonechilling bay Trusty gives when he's caught the scent.
When Lady's been taken to the pound and is visibly terrified of the rougher dogs staring at her and laughing about her collar, Peg, who's a Pekingese, steps out of the woodwork and immediately shuts the much larger, much more dangerous dogs up; it's a small thing, but to Lady it clearly meant the world.
"Hey! Hey! Hey! Lighten up, will ya?! Can't you see the poor thing's scared enough already?!"
Tramp saving Lady from a pack of feral dogs each at least twice his size.
What's more, they freeze the minute they see him.
Lady calling Tramp out for sleeping around—-sure, audiences of today may find it rather slow and sappy, but it really knocks sense into him and makes him realize he's been a jerk.
It's not character based, but the animation in the scene where Darling is rocking the cradle is stunning. Her skirt is swaying, the cradle is rocking, the bow on the cradle is moving slightly behind the cradle movement, the curtains are swaying in the breeze, the trees are moving their branches in coordination with the breeze, all at the same time. Perfectly coordinated, and done in hand drawn cell animation in 1955. Today's computer generated animation, even with masterful physics engines, don't even come close to the beauty of this scene.