That picture is exactly what the dot should look like: like an ellipse that is partially cut off to form a circle, but some of the elliptical intensity difference is still visible.
Am I reading correctly that when close up it's one dot, but when viewed from farther away it's 2 dots? And it's blurry from far away? If I'm reading correctly, then that is 100% in your eyes. Human eyes have a lot of trouble focusing on the dot, so the farther you are from the dot, the more blurry it looks. This can also result in the halos you see.
A test you can do for yourself to prove it's your eyes and not the laser: get a friend, and have him point the laser at something from far away, so that when you're standing next to him, the dot your see is blurry/messed up/whatever. Then walk up close to the dot on the wall, leaving him standing far away with the laser. As you come back close to the laser, you'll see the dot it fine and looks exactly the same, even though the laser is farther away. It's really just that your eyes have trouble seeing the dot from far away, even if the laser is fine.