
Honorable Goblin |

1) If you are invisible (as per, say, the Invisibility spell), your enemies are not Flat-Footed, they are just denied their Dexterity Bonus to AC (which happens to also happen when a creature is Flatfooted). Fortunately, a rogue still gets to apply Sneak Attack dice when attacking an enemy that is just denied their Dexterity Bonus to AC, regardless as to whether the target has the Flat-Footed condition.
2) If you are under the effects of an Invisibility spell, and attack, you become visible when your first attack is made. This means that a rogue with multiple attacks (such as from Two-Weapon Fighting or a high Base Attack Bonus) will only be able to apply SA to the first attack he makes. If he were under the effects of a Greater Invisibility spell, however, he'd be able to apply SA to all his attacks (since Greater Invisibility does not break on attacking).

reika michiko |

1) If you are invisible (as per, say, the Invisibility spell), your enemies are not Flat-Footed, they are just denied their Dexterity Bonus to AC (which happens to also happen when a creature is Flatfooted). Fortunately, a rogue still gets to apply Sneak Attack dice when attacking an enemy that is just denied their Dexterity Bonus to AC, regardless as to whether the target has the Flat-Footed condition.
2) If you are under the effects of an Invisibility spell, and attack, you become visible when your first attack is made. This means that a rogue with multiple attacks (such as from Two-Weapon Fighting or a high Base Attack Bonus) will only be able to apply SA to the first attack he makes. If he were under the effects of a Greater Invisibility spell, however, he'd be able to apply SA to all his attacks (since Greater Invisibility does not break on attacking).
I couldn't quite find the rules for this, can you point me to the correct book/quote?

concerro |

Flat-footed is a condition, just like being stunned or dazed is. It just so happens the being flat-footed denies you dex to AC. Being denied your dex bonus is what sets you up for the sneak attack.
You only get sneak attack as long as the enemy is not aware of you. After the first attack they are aware of you, because you are now visible.
We are talking about whether you get more than one sneak attack because of the invis. The answer is "no."

Honorable Goblin |
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Note that it just says "denied a Dexterity bonus to AC"; that means any time the target's denied a Dexterity bonus to AC (target's Flat-Footed, target's Pinned, the attacker is Invisible, etc).
So Flat-Footed is a condition that (among other things) denies a creature its Dexterity Bonus to AC (and thus allows a rogue to apply SA).
Pinned is another condition that (among other things) denies a creature its Dexterity Bonus to AC (and thus allows a rogue to apply SA).
Invisible is a condition that (among other things) allows a creature to ignore its target's Dexterity Bonus to AC, which is functionally identical to denying the target said bonus (and thus allows a rogue to apply SA).
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This text clearly indicates that, when you make multiple attacks in one round, they don't happen simultaneously but rather one after another.
Since the spell ends as soon as you (use your first) attack, its effects can no longer be applied to any other attacks you may make later in the round.
EDIT: See Nefreet's post above.

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in theory you could have invisibility as a contingency spell when you attack, thus allowing you to:
invisibly attack once, get sneak attack, invisibility goes down, contingency goes off, invisible again, get second attack with invisibility, and get second sneak attack... and you are then visible until another casting or you move or something to get concealment and roll a stealth roll.
In theory... it might just be cheaper and easier to get greater invisibility.