This was fun to play with for a bit. A few suggestions i have to make it more of an asshole.
One suggestion as many others suggested it would be multi-monitor support.
Have it leave random shit(like actual poop) on your screen. Could even have it shit on your cursor if you leave it idle for long periods of time.
Have it randomly lay eggs and if you don't remove the egg after a given time it hatches into another one that can do the same things. Once hatched maybe sometimes they will just be annoying and start talking to each other.
Could also have it grab a random window you have open and move it around the screen. To expand on this maybe when you are moving a window it can be an asshole and try to grab the same window you are trying to move or just be an asshole and try to steal your cursor.
Not sure how far you could take it but you could have it randomly go behind your windows(if they are covering your desktop) and start moving icons on your desktop around.
OFC you could have this all be options just incase someone doesnt like them.
Hopefully this gives you some ideas on what you could do to make it even more annoying(personally i dont find it really annoying yet).