Precision damage applies on any attack that meets the requirements of the ability that grants the damage. This includes multiple attacks made during a full attack. If conditions somehow change between multiple attacks, attacks that no longer meet the ability's requirements can't deal precision damage.
Sneak Attack: If a rogue can catch an opponent when he is unable to defend himself effectively from her attack, she can strike a vital spot for extra damage.
The rogue’s attack deals extra damage any time her target would be denied a Dexterity bonus to AC (whether the target actually has a Dexterity bonus or not), or when the rogue flanks her target. This extra damage is 1d6 at 1st level, and it increases by 1d6 every two rogue levels thereafter. Should the rogue score a critical hit with a sneak attack, this extra damage is not multiplied.
Ranged attacks can count as sneak attacks only if the target is within 30 feet.
With a sap (blackjack) or an unarmed strike, a rogue can make a sneak attack that deals nonlethal damage instead of lethal damage. She cannot use a weapon that deals lethal damage to deal nonlethal damage in a sneak attack, not even with the usual –4 penalty.
A rogue can sneak attack only living creatures with discernible anatomies—undead, constructs, oozes, plants, and incorporeal creatures lack vital areas to attack. Any creature that is immune to critical hits is not vulnerable to sneak attacks. The rogue must be able to see the target well enough to pick out a vital spot and must be able to reach such a spot. A rogue cannot sneak attack while striking a creature with concealment or striking the limbs of a creature whose vitals are beyond reach.
To deal precision damage, the attacker must see (or otherwise sense) the target accurately enough to pick out a vital spot. Any degree of concealment foils the ability to deal precision damage.
A critical hit is an attack that deals more damage, indicating a hit to a vital area.
Rage (Ex): A barbarian can fly into a rage a certain number of times per day. In a rage, a barbarian temporarily gains a +4 bonus to Strength, a +4 bonus to Constitution, and a +2 morale bonus on Will saves, but he takes a –2 penalty to Armor Class. The increase in Constitution increases the barbarian’s hit points by 2 points per level, but these hit points go away at the end of the rage when his Constitution score drops back to normal. (These extra hit points are not lost first the way temporary hit points are.) While raging, a barbarian cannot use any Charisma-, Dexterity-, or Intelligence-based skills (except for Balance, Escape Artist, Intimidate, and Ride), the Concentration skill, or any abilities that require patience or concentration, nor can he cast spells or activate magic items that require a command word, a spell trigger (such as a wand), or spell completion (such as a scroll) to function. He can use any feat he has except Combat Expertise, item creation feats, and metamagic feats. A fit of rage lasts for a number of rounds equal to 3 + the character’s (newly improved) Constitution modifier. A barbarian may prematurely end his rage. At the end of the rage, the barbarian loses the rage modifiers and restrictions and becomes fatigued (–2 penalty to Strength, –2 penalty to Dexterity, can’t charge or run) for the duration of the current encounter (unless he is a 17th-level barbarian, at which point this limitation no longer applies; see below).
A barbarian can fly into a rage only once per encounter. At 1st level he can use his rage ability once per day. At 4th level and every four levels thereafter, he can use it one additional time per day (to a maximum of six times per day at 20th level). Entering a rage takes no time itself, but a barbarian can do it only during his action, not in response to someone else’s action.
From PHB {color text}
A barbarian can fly into a screaming blood frenzy a certain number of times per day. In a rage, a barbarian gains phenomenal strength and durability
but becomes reckless and less able to defend himself.
Does it require patience or concentration to pick out a vital area?
Does a barbarian lose accuracy when raging?
If a raging barbarian makes a critical hit (i.e., strikes a vital area) - should he he get to apply precision damage?
I think there is insufficient text to support that when raging a barbarian can't apply precision damage.
Can someone please access and quote the 3.5 FAQ? I know this question has been addressed inside. Specifically, it states that a barb/rogue may still sneak attack while raging so long as the conditions are met.
From the 3.5e FAQ, pg.23:
I have a multiclass barbarian/rogue. I was wondering if he can sneak attack while raging?
Yes, provided the character’s attack meets the requirements for a sneak attack—you must have the foe flanked or the foe must somehow be denied its Dexterity bonus (if any) to Armor Class against your attack. A sneak attack requires precision (see the two previous questions), but not much in the way of patience or concentration.