When you click on the cursor when it's an arrow, does it work properly? (i.e. does it open the icon you put it on?) What about when the cursor is an hourglass -- what happens if you put it on an icon and click on it?
I've had a somewhat similar situation in which both the cursor/arrow and the cursor/hourglass allow me to click and perform the function I'm trying to do. It happens occasionally -- very sporatically, and doesn't seem to affect anything else --- I also occasionally have a boot-up situation where my cursor is completely frozen!
I don't know what causes either situation, except that occasionally a computer will have a 'corrupted' boot-up, and the sometimes the best thing to do is just to shut down and re-boot.