Being a good leader requires remembering that you're there for a reason, and the reason certainly isn't to have your way. High-integrity leaders not only welcome questioning and criticism - they insist on it.
People like to know you're listening, and something as simple as a clarification question shows not only that you are listening but that you also care about what they're saying. You'll be surprised how much respect and appreciation you gain just by asking good questions.
Regardless of the magnitude of the decision, our brains make it hard for us to keep the perspective we need to make good choices.
We hesitate to call liars out in professional environments because we feel guilty for being suspicious. Calling someone a liar for no good reason is a frightening proposition for most.
Offbeat questions are nearly impossible to prepare for, and they don't achieve the interviewer's objective - to test out-of-the-box thinking and the ability to perform under pressure. That's the bad news. The good news is that companies are moving away from them.