I have two white spaces in my inventory that can be moved around like items, but can't be interacted with in any other way. I'm told that they'll go away if I drop them in the garbage.

And I could be wrong, but I could have sworn that a bandit dropped some metal fishing poles earlier that are now nowhere to be found. Is it possible that two items are actually glitched into these white squares?

Thanks!

Edit -- I found my fishing poles, and I feel very silly for not noticing them. But the squares are still there.

So they didn't go away when you clicked a square and then the trash can?

As Lavelle said, you can use the trash can icon to remove those broken spaces.