Does it make a difference whether you spell it "her şey" or "herşey"? I see both in the dictionary, but I'm not clear if there is a difference, or if one is more proper than the other.
They are to be written separately. This is a common mistake among Turks as well (and is similar to "alot" vs. "a lot" in English).
There is a saying in Turkish for this mistake. Her şey ayrı yazılır. Every "şey" is written seperated. Meaning, if you see Şey, you hit space before it. What makes it catchy is its litteral meaning which is "Everything is written seperated."