Facial hair, glasses, dark features, horrible sleeping habits, cool hat . . . what more could one want in an arch nemesis? Also, I may or may not be able to control small animals with my mind.
just knock over my coffee, distract me from my goals, make a better joke making fun of my jokes after I make them so that I look lame, maybe steal my mail occasionally (nothing really important), tape mean notes to my door, follow me around, knock my books out of my arms at work (not if they're expensive), maybe tap my phone..
I don't know. get creative. I don't want to tell my nemesis what to do, because then I will expect it and try to thwart their thwarting.