Yes, you've had heard something! Don't beat yourself up over this. The "what could haves" will drive you nuts if you let them. Today it's the stairs, next it will be playing outside, then it will be playing soccer, then driving. Half the time, kids who fall down the steps are so relaxed, they just tumble and bounce - no that I'm recommending it , you understand, but usually it's not devastating even if it happens.
We've all done it. More than once. Most of us admit it. We've also misplaced our kids in a store, watched them run into traffic, given them the keys to the car, and a hundred other actions that prove we are human.
I suggest you go down to the hardware store and get an automatic closure attachment for doors you want to stay closed. Just be sure they aren't locking doors - if they are, change the doorknob or position a key someplace accessible so you can get back in. This applies to the outside doors when you go out to get the mail and your cheerful toddler slams the door and fiddles with the lock.
You can also get those toddler-proof doorknob covers to keep your kid from opening a door - we used them on the outside and basement doors, but also on the inside of our kid's bedroom door so he could be put in time out and had to stay there!