One major detail that has kept me from multiclassing has been the question of whether multiclassing Base attack Bonus counts for getting additional attack as part of a full-attack action.
Spellcasting DC is more clear as part of your spell DC is your caster level. I do wonder if have multiple caster classes created different "caster level Pools" or just all classes with the ability to cast stack.
You add up your primary base attack bonus (The first number) then see if you get multiple attacks from that. A barbarian 3/fighter 3 would have a primary BAB of +6, and so would get a second attack at +1, the same as a Fighter 6 or Barbarian 6.
Spell DC has nothing to do with caster level. It is based on ability scores and spell level. Still, all caster levels are separate unless they specifically say they stack (And as far as I am aware, only prestige classes have that language).