Basic Trope: A villain, Anti-Hero, or just general Jerk Ass shows that he's not so bad by doing something nice.
Straight: The Inspector Javert saves a kid, rather than capturing the Protagonist (who doesn't know about the kid, and thus is spared Moral Dissonance).
Exaggerated:
The usually violent and cold Inspector Javert saves a kid, makes funny faces to cheer him up, and even buys him candy.
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.
Downplayed: The villain sincerely thanks his minion for something, demonstrating that he's at least polite.
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.
Or, he's a Manipulative Bastard, and this is a calculated move to play mind games with the protagonist.
Petting the dog was a pretense so he could slip a USB thumbdrive (containing top secret files stolen from the Pentagon's computers) into the dog's collar and smuggle it through airport security.
It looks like he's refusing to kill a child because he's not that despicable. But then he reveals that he has no problems with killing children, he just refused to do it because it's inefficient and he gains nothing from doing so.
Double Subverted:
He lets the little girl go, but then shoots at her while she's running away. Why? Because some idiot on the other side of the line was pointing a gun at her, and that's who he was shooting.
Or he just realizes she was a demon in disguise.
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.
Enforced:
"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."
Lampshaded: The villain sees the hero, and after seeing a puppy nearby, decides to pet it while the hero watches specifically so he can make the hero doubt that he's the bad guy.
Invoked:
"See? I avoid killing puppies. That makes me not a Complete Monster!"
"If you let me go, people won't be able to hate you, because it will show them you're not a Complete Monster."
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..."
Deconstructed:
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.
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.
