At a recent tournament, the TO ruled that if a Pokémon has resistance to a particular type, and a dual-type Pokémon is that type and something else, it doesn't affect that Pokémon's attack at all. Is this true?
No. If a Pokémon has more than one type, each type still counts against the Defending Pokémon's Weaknesses or Resistances.
Source: PUI Rules Team (2004-05-20)