What is the ruling on mistakenly wearing someone else's shoes after leaving a mosque, without knowing which mosque they were taken from or who the owner of the shoes is, and should these shoes be left, or what should be done?

You took the sandal by mistake, thinking it was yours, so you are excused and incur no sin, as Allah Almighty says: "Our Lord, do not impose blame upon us if we forget or make a mistake," and as the Prophet, peace and blessings be upon him, said: "Indeed, Allah has pardoned for my Ummah their mistakes, their forgetfulness, and what they are forced to do."

However, your responsibility to guarantee it to its owner is not waived. You must return it to him if possible, and if that is not feasible, then pay its value as charity on his behalf and benefit from it. If you find its owner later, you are accountable for it, and he has the choice between the reward of the charity being his, or you paying him the value of his sandal, and the reward for your charity being yours. The possibility that the owner of the sandal took your sandal does not affect this, and you do not own his sandal by virtue of that.