There are a lot of pokemon with dual types, but I see in a lot of cases pokemon swing more towards one of the two for example Aerodactyl is a Rock/Flying pokemon, but due to its nature as a flying pokemon it is weak against electric type moves, due to its rock nature it should be immune to electric attacks but I would settle for it hit for neutral damage. Then it's also weak against its own type rock because of the its flying type and other pokemon that have the similar problems such as Nidoking, Kobuto etc...
On another note Doduo/Dodrio my be bird pokemon but unlike other bird pokemon are unable to fly, thus they should not have the advantage of levitate.
I am sure there are similar cases, but I am unaware of they so if anyone would like to throw them other there work away.