The chances of significant bugs in lean which lead to false answers to real problems are extremely small (this bug still just caused a crash, but is still bad). Many, many people try very hard to break Lean, and think about how proofs work, and fail. Is it foolproof? No. It might have flaws, it might be logic itself is inconsistent.

I often think of the ‘news level’ of a bug. A bug in most code wouldn’t be news. A bug which caused lean to claim a real proof someone cared about was true, when it wasn’t, would in the proof community the biggest news in a decade.