So until there is a screenshot, here is my general answer. As you have indicated, a visual difference is usually the indicator here. A key thing to play off of is the users mental model that an input on a page means that I can, well, input data there.
So the simple answer is make it look like (or use) a standard input once in the inline edit mode.
One key here, for my own preference, is make sure you size the area to support the border, padding etc. for the input style so that the information, and layout do not move as you go between editable fields.
The other thing to consider, if you arn't having them click edit to put everything in edit mode, is how do I know what objects are editable. My favorite pattern for this is to provide the mouseover that exposes the input like style in a faded manner. That way I am invited to click (to turn it into a input which I can edit). If you have an edit button and everything becomes editable then this is a moot point.
In this example the top is hover, the bottom is clicking in and editing.
Make sure you use the border to help create the input effect, and this is a place you can add color to indicate it is active. Also don't underestimate the ability to change the background to just off white (either with a splash of color or without) that is enough for the brain to sense, but doesn't cause the input to look odd. You can also add a tiny drop shadow to help emphasize that it is an editable input. Just don't go overboard with the drop shadow :-)