The short answer
Your team hides problems because the culture makes honesty feel risky. You can't talk your way out of that. You have to show, through your own reactions, that surfacing a mistake is safer than burying one. Do that consistently, and the hidden problems start coming to light.
You find out about problems too late because your team has quietly decided that silence is the safer bet. Research on team trust shows that psychological safety — feeling okay to speak up without punishment — is what separates teams that catch small fires early from teams that fight big ones later. Trust like that isn't built by saying 'come to me with problems.' It's built by what you do the moment someone actually does.
Marcus Aurelius noticed that people contribute to a shared outcome even when they don't fully understand what they're doing. Some work with open eyes, some without. Right now, your team is working to protect themselves — not because they want to undermine you, but because that's what the environment has taught them to do. The environment is the thing to change, not the people.
This week, pick a small mistake of your own — something real, not staged — and say it out loud in front of the team. Name what went wrong, what you missed, and what you'll do differently. Keep it short. Don't over-explain it. Then watch what happens over the next few days. When you make honesty visible and low-cost at the top, it slowly becomes possible lower down. One moment of real candor from you is worth ten 'open door' speeches.