My cats tend to leave small toys or items (favorites: socks, sweatbands and a Jerry Springer koozie) around the house when we're not at home and we find them in the hallway when we get home. What does this mean?
Cats (and all animals in general) do not understand the concepts of order or tidiness. The idea that things have a correct place to go is a human idea (and a learned idea at that).
Unless you specifically train your cat to put a specific toy in a specific place, you will always need to pick up after your cat. And your cat will probably never understand the idea that he should put things back where he got them.
They don't intend to leave those items around the house or untidy the house.
They just lose interest.
And socks, sweatbands and any sponge material; they just love this material as these things make one of their favorite activity "Clawing" fun.
One can specifically bring soft toys and even things made of soft wood for them to claw around but they will still explore new things around the house.
So just like a house with a small child in it, best way is to make sure to keep all personal belongings / fragile items out of their reach and still have lots of play-stuff filled in house which they can use to make their own world. And yes. There is no escape tidying up the house once they are done with their days share of exploring. :)
If you ask me there is no such thing as training a cat (you can train a dog for sure). You just bring a cat home and wait for her to accept you as his/her family. :) Think of yourself as his/her family and not the other way round and things will be much better.