Of course, your background beliefs are never going to be perfect, so sometimes you will reject the wrong things, but that's not because our reason is "broken" per se, it's an engineering trade-off: we have to take certain shortcuts, make certain assumptions, apply certain guesses, because working everything out in full mathematical detail just isn't possible.
(That said, I'm certainly not claiming that most people are brilliant thinkers — the line "Coming from a group of academics in the nineteen-seventies, the contention that people can’t think straight was shocking" would come as news to everyone from Aristophanes to Zamyatin.)