Marv is…kind of a dope. (To be fair, so is Harry, but Marv is less stable and even less intelligent.)
And he also has a sadistic streak a mile wide. Instead of simply robbing houses, he leaves the water running, flooding them (he does this to the house of Kevin's neighbors). As Harry puts it, Marv's "sick," and this extra-dash of property destruction is unnecessary. Check out this exchange:
HARRY: What's so funny? What are you laughing at? You did it again, didn't you? You left the water running. What's wrong with you? Why do you do that? I told you not to do it.
MARV: Harry, it's our calling card!
HARRY: Calling card.
MARV: All the great ones leave their mark. We're the Wet Bandits!
Yeah, this is messed up. Robbery ain't enough for Marv; he wants to damage property. But these destructive tendencies are actually what indict Marv and Harry, in the end. When the cops finally arrest them, they know all the houses Marv and Harry have hit because of ye olde Wet Bandits calling card. And the boys in blue are able to send Harry and Marv away for a good long time.
But, before that happens, we get to see Marv lose his cool when Kevin fakes him out with the Angels with Filthy Souls video. Marv thinks an actual gangster is shooting another in Kevin's kitchen, though Harry rightfully finds this suspicious.
Finally, he goes through Kevin's maze of booby traps—getting hit with a clothing iron, stepping on a nail, and shredding his feet on Christmas ornaments (among other injuries). He also beats Harry with a crowbar in an attempt to kill Buzz's tarantula.
…and you thought karma didn't exist.
This makes it clear that Marv isn't cool under pressure. He immediately freaks out when he sees the tarantula, and needlessly smacks his partner with a blunt instrument. He isn't exactly a criminal mastermind, to put it mildly.
If Kevin's enemies had been geniuses, he might have been little overmatched. Fortunately, they're anything but.
In the end, after catching Kevin and then getting knocked out by Marley's snow-shovel, Marv is arrested along with Harry. They're going away for a long-time…or, actually, just for two years, since they reappear in Home Alone 2: Lost in New York.