@Neuro Fuzzy - That is interesting, and it got me thinking, and I think your dad is wrong. We all know Dad's are never wrong, so in this instance, let's assume he was just sleepy.

I'm not being pedantic here, it just got me curious and I had to think about it ...
In order for you to see the dot, you need to see the reflection of the light on the moon's surface. The light therefore has to travel from you to the moon and then back. Then you move the pen almost instantly to point other side of the moon. The light travels to the moon and back again, so you can see it.
In a perfect instantly fast scenario, where you can move the pen instantly, to observe the laser dot moving from one side of the moon to the other, light has to travel from you to the moon and back twice. That distance travelled fast exceeds the diameter of the moon, and thus light could travel from one side of the moon to the other far faster than you could observe a dot from a laser pen moving across it surface.
The same goes for any scenario. Light travels faster from A->B than it does from O->A->O->B->O, where O is the position of the observer. Even if you didn't wait to observe the first dot, and you moved the light from A->B instantly, choosing to observe both dots at the same time, the time taken would still be O->A->O (or) O->B->O (which ever is longer) to observe both dots. Where ever you stand at 'O', it will always take longer, unless you stand exactly between A and B, and then it'll take exactly the same time.
Damn, what a waste of 10 minutes that was. Must do work ...