Big Mistake
noun
A 間違い is a mistake. A big mistake is a big mistake.
大間違い is less about factual errors and more about someone being way off in their assumptions or expectations. It suggests things didn't go according to plan — like you assumed a smile would fix everything or expected a date to go well, only for things to turn out completely wrong.
The reading is 大 and 間違い put together into one not so mistaken word.
ニコニコ笑っておけば何とかなるでしょって思ってる人は大間違いですよ。
Those who think they can get by if they just smile and laugh are very mistaken.
そもそも、野外で録音しようとしたのが大間違いだった。
The original big mistake was that we tried to record outdoors.
これで夏が終わったと思ったら大間違いだよ！本当の夏は、まだまだこれからなんだから。
If you think this is the end of summer, you are mistaken! The real summer is yet to come.
彼女をデートに誘ったが、それは大間違いだった。
I asked her to go out with me, but it was a big mistake.