To Be Decided...
Ok... after reading through the rulebook again, and letting it sink in for a few more days... I'll have to wait for an official ruling on the PTFG Web site or a future rulebook.
Before I go into it let me restate the rulebook rule (pg. 8 "Altering Attacks):
"Some effects change the damage a Pokemon does. If an effect adds or subtracts damage, it only changes attacks that actually do damage. For example, if a Pokemon has an effect that multiplies the damage its attack does, and it spins a Miss or a Blue, there isn't any damage (there would be no effect to the Miss or Blue)."
Now I believe the last sentence in which it said there would be no effect to the Miss or Blue is referring to the original effect of the attack that's looking to be modified, meaning the effect doesn't trigger because it was not a damage based attack. We all agree on this, I think. BUT... this wording could mean one of two things happen. It could mean the non-damage attack resolves or it doesn't resolve because, in order for the effect to trigger (from the initial spin of swords dance), the immediately successive spin must be a damage based attack.
There's a big statement going for the successful resolution of Dodge after spinning swords dance, "If an effect adds or subtracts damage, it only changes attacks that actually do damage." That statement right there tells me if it's another attack (that doesn't do damage) after the initial attack and effect (swords dance in this case) it will not be changed (a miss or blue). An effect only "changes" attacks that actually do damage. It's clear a dodge doesn't do damage, so the effect of swords dance does not trigger or change the attack.
BUT...
It could be argued that "change" refers to damage related attacks and it is merely a reiteration of common sense (you cannot multiply damage of an attack that does no damage), still leaving the problem of resolution (does the effect not triggering mean the attack is over and it does no damage or do you resolve the non-damage attack?) However, I would think they makers wouldn't need to reiterate common sense. I would only think they'd need to qualify the rules and disambiguate them if necessary. However, they didn't disambiguate the resolution of the attack after spinning the effect, still leaving the rule up for interpretation pending an official PTFG ruling on their Web site or in future editions of the rulebook.
All the makers would need to do to fix this confusion is add a qualifying statement after the last sentence of the ruling I listed that says "there would be no effect to the Miss or Blue and those attacks (Miss or Blue) resolve as they would without the effect" or "If an effect that would multiply damage on successive spins does not result in an attack that does damage immediately after the effect, it does not resolve and the attack does 0 damage.