Do you keep your nursery room door open or closed at night? I assume by a certain age, you'll have to keep it closed just so LO doesn't get woken up, but when they are really little?

I've been leaving it open/cracked at least. Meanwhile, DH always wants to close our bedroom door. After tonight's MOTN feeding, I realized he left the guest bedroom's windows open and living room windows opened. We only have one floor in our house. Even though it's a really safe city we live in, I couldn't help but suddenly feel paranoid (and annoyed with DH!). If our door is closed and baby's is open and windows are open, how easy would it be for someone to come in and we wouldn't notice? Granted I have my video monitor on, but still.
Of course I shut all the windows and turned on out night alarm which I've only used before when I was home alone. And of course I haven't gone back to sleep yet thinking about this.

What do you do about your bedroom door and nursery door?