What is the correct way to iterate over multivalue items of a form element in D7?
element_children() returns any array's key that doesn't start with #, used for properties in form API arrays, and in rendering arrays. It doesn't return numeric keys, as the function would pass to your code an array key such as "item", for example.

Instead of using the constant LANGUAGE_NONE, I would use field_get_items(), which returns the values for the language currently set for the field, which could not be for the LANGUAGE_NONE language.