Unfortunately, "Brain Farts" are an everpresent malady we all have to be ever vigilant about. Just as important as avoiding them, is understanding how best to deal with them when they happen. Just as no matter how hard you suck on an inadvertent whistle won't bring the "tweet" back, a brain fart needs to be immediately dealt with.
Hopefully the entire crew you're working with is paying attention to each other's actions and is comfortable with discretely questioning something they're not in agreement with. Of course it's just as important each crew member is just as comfortable being discretely questioned and won't be offended or defensive.
Being questioned is a win/win situation. It either gives you the opportunity to prove how smart you are, or makes you aware of a mistake, so you can correctly deal with it. Listen to the questions you may be asked, and really think about the answers you give. When you realize it was an actual brain fart, accept that reality and if possible correct it. If you can't correct it, own up to it and (the hard part) explain the mistake to both head coaches.