This happens in various games, and not just in games. It is most likely a hardware related issue. There are a few things you can do to either fix this, or confirm what is causing it.
Before doing anything, update your video card drivers. Visit your video card manufacturers website and download the latest drivers.
If the problem persists, you can boot into safe mode and try to reproduce the problem. Seeing as in your particular case the problem only occurs while playing Starcraft 2, you may not be able to reproduce the problem. However, if you do reproduce the problem, there's a very good chance your video card is on its way out (AKA it's dying). If you don't want to purchase a new one, you can wait and see if it dies, and just live with the issue.
One last thing you can try is to change the Window's mouse style. I don't own SC2, so I don't know if it uses a custom mouse. But it's a simple change and worth a shot!
However, one thing seems clear: This isn't Starcraft 2 related, or even video game related. It is probably OS or hardware related. You can try and Google this yourself and see if you can find any solutions. It seems to me like the memory where the cursor is stored is being corrupted, causing it to draw incorrect information. This behavior may be triggered by SC2, but the problem lies within the video card memory.
In response to Ender (I cannot post comments yet!):
The reason I say that the video card may be starting to 'die' is because artifacts like this appear when your card gets old and is ready to go. This is a graphical glitch that is not game dependent, or OS dependent, because I've seen it on XP and Windows 7. That leaves the video card to blame (I rule out the actual image file begin corrupted because this will happen with any cursor image). Before my old graphics card died, weird things like this would happen. I would get textures in games that were offset, and you got strange lines and dots in them. Some textures would also discolor, and I'd even get polygons ripping across the screen. After this, my video card died, and I had to purchase a new one.
Without proper image of the cursor in its glitched state, its hard to tell. A possibility is that one of these artifacts causes the cursor to shrink into a bunch of very small cursors. They would appear as a line of very small dots. Things like this I have also seen appear in games when your card is on its last legs.