It's not that feinting can't be used against mindless foes, it's that feint can't be used against foes that lack an intelligence score (which is usually mindless, but not always).
Feint wrote:
Feinting is a standard action. To feint, make a Bluff skill check. The DC of this check is equal to 10 + your opponent’s base attack bonus + your opponent’s Wisdom modifier. If your opponent is trained in Sense Motive, the DC is instead equal to 10 + your opponent’s Sense Motive bonus, if higher. If successful, the next melee attack you make against the target does not allow him to use his Dexterity bonus to AC (if any). This attack must be made on or before your next turn.
When feinting against a non-humanoid you take a –4 penalty. Against a creature of animal Intelligence (1 or 2), you take a –8 penalty. Against a creature lacking an Intelligence score, it’s impossible. Feinting in combat does not provoke attacks of opportunity.
It won't gain the mind-affecting descriptor if it's a mind-affecting effect from a feat (it's a feat not a spell), instead it will call out that it's mind-affecting.
This is a feat that is mind-affecting.
Antagonize wrote:
Whether with biting remarks or hurtful words, you are adept at making creatures angry with you.
Benefit: You can make Diplomacy and Intimidate checks to make creatures respond to you with hostility. No matter which skill you use, antagonizing a creature takes a standard action that does not provoke attacks of opportunity, and has a DC equal to 10 + the target’s Hit Dice + the target’s Wisdom modifier. You cannot make this check against a creature that does not understand you or has an Intelligence score of 3 or lower. Before you make these checks, you may make a Sense Motive check (DC 20) as a swift action to gain an insight bonus on these Diplomacy or Intimidate checks equal to your Charisma bonus until the end of your next turn. The benefits you gain for this check depend on the skill you use. This is a mind-affecting effect.
Diplomacy: You fluster your enemy. For the next minute, the target takes a –2 penalty on all attacks rolls made against creatures other than you and has a 10% spell failure chance on all spells that do not target you or that have you within their area of effect.
Intimidate: The creature flies into a rage. On its next turn, the target must attempt to make a melee attack against you, make a ranged attack against you, target you with a spell, or include you in the area of a spell. The effect ends if the creature is prevented from attacking you or attempting to do so would harm it (for example, if you are on the other side of a chasm or a wall of fire). If it cannot attack you on its turn, you may make the check again as an immediate action to extend the effect for 1 round (but cannot extend it thereafter). The effect ends as soon as the creature attacks you. Once you have targeted a creature with this ability, you cannot target it again for 1 day.
This is a feat that is not, note the lack of a mind-effecting language.
Call out wrote:
A well-crafted insult forces an opponent to duel you.
Benefit(s) As a standard action, you can make an Intimidate check against a hostile target within 30 feet that can clearly see and hear you. The DC of this check is equal to 10 + your opponent’s Hit Dice + its Wisdom modifier. If the target is trained in Sense Motive, the DC is instead equal to 10 + your opponent’s Sense Motive bonus, if higher. If you succeed at this check, the target enters a duel with you. The target cannot withdraw from the duel for 1 round + 1 round for every 5 by which the check beat the DC.
Some more mind-affecting feats
Deadhand Style wrote:
Your study of death allow you to exploit your foes’ fears.
Prerequisite(s): Wis 15, Improved Unarmed Strike, Knowledge (religion) 4 ranks, ki pool class feature, nongood alignment.
Benefit(s): While using this style, if you have at least 1 point in your ki pool, you gain a +2 bonus on saves against fear effects, and the DC of Intimidate checks against you increases by 4. As a swift action, you can spend 1 point from your ki pool to empower your unarmed strikes. Creatures hit with your unarmed strikes must succeed at a Will save (DC = 10 + 1/2 your character level + your Wisdom modifier) or become shaken for a number of rounds equal to your Wisdom modifier. This is a mind-affecting fear effect.
Frightful Shape wrote:
Your wild shape form strikes fear into your opponents.
Prerequisites: Wis 19, base attack bonus +9, wild shape class feature.
Benefit: When you use wild shape, it is supernaturally ferocious and disquieting in appearance, such that when you attack a creature, you can use this ferocity to frighten observers. Opponents within 30 feet of you when you attack must succeed at a Will save (DC = 10 + half your character level + your Charisma modifier) to resist being affected by your frightful shape. On a failed save, creatures with fewer Hit Dice than you become shaken, or panicked if they have 4 Hit Dice or fewer; in either case, the effect lasts for a number of rounds equal to your character level. An opponent that succeeds at its saving throw is immune to your frightful shape for 24 hours. This is a mind-affecting fear effect.
Broken-Wing Gambit lacks this language, therefore it is not a mind-affecting effect and RAW works against (with?) the creature.
