After Knuckles saves Rouge from falling to her death, not only does he apologize for hurting her, but just before she leaves, Rouge glances back at him with a smile on her face.
There's also a moment where Shadow rescues Rouge because she reminds him of Maria.
Right after Knuckles saves Rouge there is a long moment... before she angrily yanks her hand away.
In the scene before the Final Rush stage, Knuckles sees Sonic appearing right before him dropping to the ground and comes to check on him. Sonic explains that he used Chaos Control with the fake Emerald to escape the exploding capsule Eggman trapped him with. Knuckles picks him up on his shoulder, asking him if he's okay. This scene pretty much shows that despite their differences, the two do look out for each other.