Black puddings are immune to slashing damage, and the Corrosive Form trait states:
... Any nonmagical weapon made of metal or wood that hits the pudding corrodes. After dealing damage, the weapon takes a permanent and cumulative-1 penalty to damage rolls. ...
The bit that confuses me is "after dealing damage". If the pudding is immune to slashing damage, then slashing weapons will never deal damage, and thus should not take the -1 penalty. However, that seems to contradict the previous statement, that anything that hits will corrode.