Splash Potions do not give effects

When trying to cure a zombie in survival mode, the splash potion of weakness did not effect me or the zombie. I tested in a fresh superflat world, and no player-thrown splash potions caused any effects on mobs or the player, either in creative or survival mode.
Update: I just spawned a handful of witches, and stood there in survival mode while they showered me with potions: no effect.