I was at a quiz once, where they asked "Which British football team is mentioned in the Bible?"
Another good one along a kind of similar vein is "In the original Band Aid recording of 'Do They Know It's Christmas', which performer sings their own name?"
We also had a frustrating question at a community quiz we took part in, where the question was "Rum, Eigg and Muck are part of which Scottish island group?" We put 'The Small Isles' and were told we were wrong, as the answer was 'The Hebrides'. The quizmaster quite 'helpfully' informed us that yes, they are quite small islands, but they're actually part of the Hebrides.
No amount of protesting that they were indeed a part of the Hebrides, but part of a group known specifically as the Small Isles - so either answer should actually have been fairly accepted - would convince him that we were right. We asked him to look it up online, but he said that phones were not allowed; erm, I think it's OK if it's the end of the quiz and you're the quizmaster!!
It was a crucial point and we came second because of that question, when it should have been a tie-breaker for first place.