Gus Polinski offering Kate a lift after discovering that she needs to get to Chicago.
When Kevin meets the guy dressed as Santa Claus, he asks for his family back namely his mother, father, brothers and sisters and if Santa has time, Uncle Frank. Even though Uncle Frank is a massive Jerkass to Kevin, he still has a place in Kevin's heart.
It's a small moment, but Santa giving Kevin some Tic Tacs because he's out of candy canes is incredibly sweet, since he believes "Everyone who sees Santa should get a little something."
Kevin talking to Old Man Marley in church, discovering he's actually quite a nice man despite all the scary rumors.
Kevin's mother Kate being comforted by the Polka King while constantly calling herself a terrible mother.
Kevin and his mother reuniting at the end of the first film. Made even better when the rest of the family walks through the door seconds later.
Old Man Marley reconciling with his son and reuniting with his family, which Kevin witnesses.
Add in Marley giving Kevin a thankful wave, as Kevin was the one to suggest that Marley actually call his son and try to make amends.
Buzz praising Kevin for not burning the house down while they were gone.
A few Deleted Scenes show that, despite being jerks to him in the beginning of the film, Megan, Linnie, and Jeff do love Kevin and spend most of their stay in Paris worrying about him. In the Paris scene, Megan is clearly worried about Kevin and voicing her concerns to Buzz, who just plain doesn't care.
In another deleted scene, Linnie finds that Peter is unable to sleep since he too is worried about Kevin. They then share a heartfelt moment on why they both think togetherness is so important at Christmastime.
In another Deleted Scene, we see Harry and Marv joking around in the van. This suggests that despite their occasional bickering, they appear to have a genuine Villainous Friendship.
Home Alone 2
Buzz's heartfelt speech/apology to Kevin. He's actually kind of a nice kid, when not acting like a total dick.
The first time and the second time we hear "Christmas Star". The first time was with Kevin missing his family once again while looking at a view of New York at night. What adds to the heartwarming is that he says goodnight to his mother, while at the same time in the Florida Resort Kate is saying goodnight to Kevin. The second time was before he decides to deal with Harry and Marv. He makes a stop at the Beth Israel Hospital Children's wing. A sick kid looking out the window waves to Kevin, who waves back. This motivates him to stop Harry and Marv from robbing the toy store, since the proceeds are supposed to go the hospital.
Buzz giving Kevin the first present to open on Christmas morning.
Uncle Frank cheering for Kevin shortly afterward. Nice to see after he spent the first two movies being a complete ass to him.
Although he's giving away his father's money, Kevin donating money to the hospital was a sweet gesture.
Kevin thanking the Pigeon Lady for saving his life, followed by the lady blowing a kiss to him.
Kevin giving the second turtledove ornament to the Pigeon Lady.
Kevin's relationship with the Pigeon Lady is this, being he convinces her to not be so closed up, telling her that you're going to be hurt sooner or later, but shows you're alive. Especially heartwarming in the end when he gives her a turtle dove and says they'll be friends forever. Daaaw.
Harry's promise to take Marv to the Central Park Zoo when they have time to kill before the heist. Nice to see him doing something nice for what we might assume is his only friend.
Home Alone 3
Alex getting rewarded for his role in catching the gang, as well as getting respect from his family for it (in contrast to Kevin's, who didn't know about Harry and Marv), who don't even seem to care too much about any of the damage his traps caused to the house (no doubt because of said reward).