I am not sure if what you are "seeing" is only occuring in "offline" mode as I see it in both online mode also.
That being said what you are seeing is how QS draws points using the tool you chose to draw with. It will put a point where you click. If you clicked once to start a line, then once more to finish it, you will get two points. The rectangle gives you the same thing, a point per click; you have to click 5 times to get the 4 lines of the rectangle.