By this I mean if you use a power that has both the weapon and spell tag, does the weapon's accuracy get applied twice if it is a catalyst, or does the weapon's accuracy bonus only get applied once per power? Thanks!
It should only apply once. All the abilities with both of those tags are (IIRC) phrased along the lines of 'Do a weapon attack that adds [formula] bonus [element] damage' and may or may not have other effects, so it should be treated as a weapon attack and not double-dip on the bonuses. The Spell tag would just be there to indicate that it's a power that requires both a weapon and the ability to cast to work, ie it can be shut down with either Disarmed or Silenced. See this discussion which seems to bear this out; Powers with both tags are treated as weapon attacks for calculation purposes, the spell effect is secondary.