Direct Quotes from http://paizo.com/pathfinderRPG/prd/: (emphasis mine)
Uncanny Dodge (Ex): At 2nd level, a barbarian gains the ability to react to danger before her senses would normally allow her to do so. She cannot be caught flat-footed, even if the attacker is invisible. She still loses her Dexterity bonus to AC if immobilized. A barbarian with this ability can still lose her Dexterity bonus to AC if an opponent successfully uses the feint action against her.
Invisible: Invisible creatures are visually undetectable. An invisible creature gains a +2 bonus on attack rolls against sighted opponents, and ignores its opponents' Dexterity bonuses to AC (if any).
My question: Do you get your dexterity bonus against an invisible foe when you have uncanny dodge or not?
Invisibility does not specifically say that it makes the opponent you attack flat-footed, only that it denies them their dexterity bonus to their AC (which is not the same thing). However, Uncanny Dodge specifically mentions invisibility, suggesting that you get some bonus against it. So, as far as I can tell, either the wording is off and uncanny dodge allows you your dexterity bonus against invisibility, or paizo felt it necessary to point out that uncanny dodge keeps you from being caught flat-footed even if your opponent is invisible, for no reason other than to mention it (possibly for clarity).