When a character in a story I'm reading says or does something inconsistent with his or her established beliefs or behavior, I place a bookmark, then watch for the why of that odd statement or action. If it never shows up, I put a big black mark next to the author's name.
In the course of my own work, when a character speaks or acts inconsistently, I also put in a bookmark, to remind myself I need to sort out the oddity. Sometimes, it turns out the character is trying to fool another character. Sometimes, the character's trying to fool him/herself. Sometimes, especially in early drafts, I think I've heard one character speak, when in fact the words came from someone else. Sometimes, I've misunderstood the character. All these possibilities are fine, so long as the variant information is resolved. If a raging white racial bigot takes a little black boy into a confectionary, buys him an ice-cream cone, then sends him on his way with an avuncular pat on the back, it's my job to dig out the reason, and make sure the reader is similarly enlightened before The End.
This necessity also translates out to real-life situations. Taking into account that people do not act out of character without reason may prevent painful misunderstandings.
Many years ago, my friend, Graham Webb, a dealer in antique music boxes in England, called to offer me a very impressive Swiss cylinder box. I told Graham I was very much interested, but would need to sell some of my other music boxes to pay for this one. There was a major swap meet coming up in a week: could he put the box on hold for me until that time? He said he'd be happy to.
The swap meet was successful, and immediately afterward, I called Graham, identified myself, and told him I would in fact like to buy the Nicole Grand Format Overture Box. To my surprise and dismay, he said, in a very cold tone, "I'm sorry. That box is sold."
Understand a hard-core collector's reaction. I was just this far from giving Graham two earsful of anger and indignation when a voice in my mind reminded me how long I'd known him, and how out of character his comment was. There had to be a reason. So I took a deep breath, and said, "Graham, I thought you told me you'd be holding that box for me."
There was a moment of silence, then, "I'm sorry...who did you say this is?"
"Larry," I said. "Larry Karp."
That brought a burst of laughter. "Oh, Larry, hello. I thought you said 'Barry Clark.' These transcontinental phone lines, you know. Just terrible."
From that time forward, I was always 'Barry" to Graham, and we never stopped chuckling over the Great Big Transcontinental Misunderstanding.