I sat down with a buddy to do some village science.
Duck Hunt: You can pocket the can; unpocketing it tosses it in a small grenade arc, and it explodes upon contact with anything. Tossing it while standing and neglecting to move afterwards places you in the blast radius, so watch out for that.
You can pocket clays.
You can't pocket the Wild Gunman, but you can pluck their bullets out of midair.
Villager: In addition to being able to pocket the tree, you can also pocket one chunk of the water from the watering can. It's not enough to grow a tree or meaningfully push anyone so I have no idea why you'd want to, but the option exists. Is stealing one block enough to prevent the tree from growing?
(edit: Some megaman players like to toss out jab pellets at villager just to try to trick him into pocketing one on accident, so against another villager you could try to clog up their pockets with water, maybe?)
Despite the fact that Fox can reflect upsmash fireworks, the pocket can't pick them up.
Palutena: You can pocket Holotarget lasers, though if you're still in the way of the rest of the burst you'll be cancelled and get nothing. The bullets retain the angle they were fired at; if Palutena was shooting up at you, you'll get a bullet that, when unpocketed, flies away at a 45 degree angle.
You can pocket Celestial Fireworks.
You cannot pocket the reflect wall.
Ness: You can pocket PK Thunder. It flies directly forward when unpocketed.
You can pocket PK Fire.
You cannot pocket PK Flash.
Rob: You can pocket gyromite, as well as the charge laser, though I imagine these are obvious.
Falco: You cannot pocket reflector.
Zelda: You cannot pocket Din's Fire. (TRAGEDY)