If a villager throws potatoes, none of the villagers or the player can pick up them

Try replacing all the villagers, because villagers from previous versions can't pick up items (such as potatoes).

I'm in a brand new world, and there are getting to be a lot of potatoes floating around. If the villagers were unable to pick them up, I'd think they'd be unable to throw them. Also, I can't pick them up. I thought they were somehow being uprooted at ground level and being actually on the ground but showing in the wrong place, (I'm underground), but I went up above and can't get them there, either. Also, they're not just under the farms. I've only seen potatoes, but I don't know how often the villagers throw stuff around.

Actually it's once their inventory gets to 60. They have more inventory space than that but once they have 60 items they stop picking things up for some reason. As for how they get on the ground, they throw excess food at damaged villagers to help them heal. Which doesn't happen if their inventory is too full. The dropped items can be picked up in the last 5 seconds before they despawn btw, which isn't that helpful with no way to tell when they're close.