Unity 4.3.4 2D mode, hide mouse pointer only works on half of the screen

I am starting Unity3D today, but I am familiar with C# though.

I am following a 2D game tutorial at Udemy.com, and I am trying to hide the mouse cursor.

So I did this,

     // Use this for initialization
     void Start()
     {
         Screen.showCursor = false;
     }
 
     // Update is called once per frame
     void Update()
     {
         Screen.showCursor = false;
     }

But the mouse cursor is hidden at about half of the screen only (on the left side). If I move my mouse to the right the mouse pointer appears, if I move back to the left the mouse pointer disappears.

I am thinking this must be related to the way I setup my camera or view or something, any ideas what I should look at?

Update 1: Looks like the mouse is hidden at certain rectangle area of the screen but not the others. My initial description (half of the screen) is not accurate.

Update 2: I know what is happening now, it depends on the screen resolution I select!. If I select 800x600 then only a certain portion of the screen will the mouse get hidden. If I select Free Aspect then almost all the screen area will work as intended. See screenshot.

But I don't know whether it is a bug in Unity game player or my code. I assume it is a bug in the player since I have not done much coding at all.