My guess is the intent is that you get the DR per attack.
Anybody send this to WotC as a question?
Personally, I'd rather apply Resist all once per damage type rather than once per attack because the per attack interpretation can result in some odd corner cases.
For example, consider the power invoked devastation (Invoker Attack 29, Divine Power). The user makes a single attack roll and compares the result against each target's Fortitude, Reflex and Will defenses. If the attack roll exceeds the target's Fortitude, it takes force damage and ongoing cold damage. If the attack roll exceeds the target's Reflex, it takes lightning damage and ongoing fire damage. If the attack roll exceeds the target's Will, it takes radiant damage and ongoing psychic damage. Is this considered one or three attacks? If this is considered one attack, than you get the odd case that the attacks would be resisted separately if the power had been worded so that the user made a separate attack roll against each defense.
Compare this example with the deathrattle viper (L5 Brute, MM), which has a bite attack that deals untyped damage and the target is subject to a secondary attack which deals poison damage. Is this considered one or two attacks? If it is considered two attacks, then you get the odd case that resistance would have been applied only once if the viper's bite dealt untyped damage plus poison damage, such as an ixitxachitl demon ray's (L3 Skirmisher, Demonomicon) tail barb.
There's already a mechanic for "Resist 5 fire, cold, acid, lightning, thunder, radiant, necrotic, poison." It's listed as "Resist 5 fire, Resist 5 cold, resist 5 acid, resist 5 lightning, resist 5 thunder, resist 5 radiant, resist 5 necrotic, resist 5 poison."So if I fall in an elemental pool and take 8 fire, 8 cold, 8 acid damage, and have resist 5 fire and cold, I take 3+3+8=14 damage, but if I have resist 5 fire, cold, acid, lightning, thunder, radiant, necrotic, poison, and everything else under the sun (i.e. resist 5 all), I take 3+8+8=19 damage? I don't think that's right. Resist 5 all means resist 5 all, not resist 5 one out of three.
Resistances should never stack. Having resist 5 x and resist 5 y against an attack that does damage of type x and y means you only resist 5.
We all agree on that, yes?
So, having resist 5 x and resist 5 x _again_ shouldn't stack either.
I think we can agree on that.
Now, say you take 5 fire + 5 cold and have resist 5 fire and resist 5 all. Some of the comments here suggest you should apply the resist all only once, to the cold damage, and you'd have to apply the fire resist to the fire damage, so that you can take no damage.
What if you have two separate sources of resist 5 all?
That shouldn't work. You can't stack resistances, and there isn't suppose to be any added benefit from having multiple instances of the same effect.
And yet, if the "apply each resist to any part of the attack once" theory is correct, then having multiples of resit all SHOULD help. I think that's wrong by RAI, and so I'm drawn to the argument that resist 5 all, versus a 5 fire + 5 cold attack, deals 0 damage, because you can only benefit from one resist all and so it should apply to every damage group. It's the only thing that's consistent.
A similar argument can be made from the opposite side, for an attack that does the same damage type twice, such as 5 fire + 5 fire: could you use MULTIPLE resist 5 fires to negate it? Because you're not suppose to get more than one.
So I say, an attack that does 5 cold + 5 fire + 5 acid + 5 lightning, does zero damage to a target with resist 5 all.
(But to reiterate a half dozen other comments, this style of damage has seriously fallen out of favor since MM1, so it's probably not a big deal in practice.)