
Saethori |

Nothing Can Stop Me (Ex): Once per round, while the vigilante is moving, he can make one attack as a free action against an unattended object in the way of his path, such as a door or table. If his attack deals enough damage to destroy the object, he can continue to move. If he doesn't destroy the object, his move ends. This attack is made as part of his move action and doesn't count against his attacks this round. If his attack inadvertently targets a creature (such as a mimic), it automatically misses and his move ends (although he can still attack the creature as normal at the end of his movement). Only an avenger vigilante can select this talent.
The text states the attack is made as part of the move action. This means he cannot make it during a charge, mounted or otherwise, as these are special actions and don't use the move action specifically.

Secret Wizard |

Also you can't charge something you can't see it are obstructed (door in the way).
This is for the "enemy sees us, closes a door" so you don't need to move, open door, move, attack. You can move, free action open, attack.
In my table, we allow blind charges, but if you don't find a target by the time your maximum movement is through, you are considered to have taken the Run action instead (and can continue with that movement if you'd have more available).

Lord Twitchiopolis |

Also you can't charge something you can't see it are obstructed (door in the way).
This is for the "enemy sees us, closes a door" so you don't need to move, open door, move, attack. You can move, free action open, attack.
Normally I agree with you 100%, BUT
If his attack deals enough damage to destroy the object, he can continue to move.
Seems to imply that the intent is for the movement to continue unimpeded.
In the end, I still agree with you, but only 95%.It's a poorly worded ability.