I think that messing with Vault City's computer terminal with a dumb character made me break in tears (the thing about a woman's voice, the 'dead snakes', and the final zap).
Also, talking to Ms. Bishop with a Dumb One is hilarious as well. The "[stare at boobs and drool.]" line, the Ian reference ... makes for a great laugh.
Hell, the way the game describes slot machines to stupid characters as "boxes with three eyes and an arm", the dialogue with Torr, reading the bulletins (or at least trying), not knowing what the hell is going on when something blatantly obvious is happening, the Forrest Gump references ... goddammit, just the fact that the Chosen One is dumb.