An irredeemably evil villain stops his evil plans just to help an elderly woman cross the street, rescue a cat stuck in a tree, give a million dollars to a homeless person, and buy an ice cream cone for a sad child.
The villain sincerely thanks his minion for something, demonstrating that he's at least polite.
A Jerk Ass apologizes after he sees that he hurt someone's feelings.
During a footchase with the Protagonist, Inspector Javert slows down so he does not push over a kid, even if it risk him getting away.
Justified: The character may have flaws and bad traits but he is still capable of doing nice things and is not against doing nice things as long as they don't interfere with his ultimate goal.
Parodied: The villain laughs maniacally as he watches a city burn by his own doing, and then abruptly stops as he sees a puppy dog and proceed to cuddle and feed him.
Zig Zagged: The villain lets the little girl go, but then shoots her. But then it turns out she was actually a demon in disguise. Then it turns out the demon was also a child and a Noble Demon to boot, so they're not evil. Then it turns out that the Noble Demon was being controlled by an Eldritch Abomination, but then that turns out to be Not Evil, Just Misunderstood...
Averted: The villain has nothing to do with any kind of dog.
"Given that this guy's going to do a Heel-Face Turn later, we need to set up that he's not such a bad person now."
Discussed: "Well, that guy stopped to save a kitten before he flooded the town, so he'd probably be easier to talk to about this even worse guy than the guy who burned down the orphanage.
Conversed: "I'm trying to find a way to show people that I'm not just about oppression. Should I adopt an orphan or something? Dictators with hearts in shows are always adopting kids or puppies or cute little kittens..."
This used to present the idea that absolute moral judgement is not possible, shifting the setting to full-on Grey and Gray Morality.
Alternatively, what the Doctor said about this sort of behavior and what it says about the villain in question: "You let one of them go, but that's nothing new. Every now and then, a little victim's spared... because she smiled, cos he's got freckles, cos they begged. And that's how you live with yourself, that's how you slaughter millions, because once in a while, on a whim, if the wind's in the right direction, you happen to be kind."
Reconstructed: He does little acts of kindness because if absolutely moral purity is not possible, neither is absolute moral evil. Alternately, using the Doctor's take on it, the villain in question really does feel conflicted about his actions and they may even lead to a Heel-Face Turn.