Dual-type moves could always only take one STAB/Weakness/Resistance into account. A Water/Ground move would grant STAB to Water, Ground and Water/Ground Pokemon but in the case of the latter it would only be x2 STAB. For weaknesses and resistances, it would count as x2 or 1/2 (x4 or 1/4 on Pokemon that are doubly weak to Water or Ground) damage no matter whether the Pokemon is weak to Water, Ground or both.
It would promote move and Pokemon versatility without being so overpowered that it destroys everything. For example Muddy Water can be picked over Surf because it allows Water-types to get STAB on a move strong against Electric-types, but it also means that Flying-types are immune.
It could make some Pokemon a lot better if done correctly, particularly with types such as Poison and Steel that are somewhat lacking offensively. If Sludge Wave became a Poison/Water move then it would allow pure Poison-types to get STAB on a move against Fire-, Ground- and Rock-types.
I would most definitely 8238324345678921398235346534532467486554235345345099234923884934234832485% sure give up on Gen 6 and the series if it was possible to do 16x damage on Graveler with a Water/Grass move.
I would most definitely 23459734572930947289432745% give up on Gen 6 and the series if there was a new type that would change the old mons.
I loathe Gen V. I am being optimistic for Gen VI, because I hope they can make a good new feature.
One would guess if a attack with say fire/electric type with say for example 100 base that 50 base would be fire an the other 50 would be electric.... That's what I believe a smart person would think it would be more like rather than oh no I'm weak to one, resist vs one of the types so I take x2/4 damage at 100 base attack soooo op oh no.....
Instead of ok hmm I'm resist vs that so that's 1/2 of 50 base, an weak vs that so 2x of 50 base....
Wow that was so hard to figure out or try to comprehend, mind blown