For like 20-30 seconds at a time (some places, like my lap or his pram, for like 5 minutes, but there are places to catch himself if he starts leaning in both those spots.)
Also, what's with the arm flapping? It seems almost compulsive when he's tired, and I get bopped in the face OVER and OVER and OVER and OVER in the mornings (he comes in with us after 7:30, when he gets up - we play for a while then we all go back to sleep for about an hour at 8:30 or so.) And I'm usually too tired to move my face, so I put up with it.
Also, I had him on my back in a wrap today, and he puked in my hair! Aaugh! Here is a piece of wisdom for you: do not flip a baby up on your back and tie him there tightly squished against you when he's just eaten like 5 oz of milk!! Unless you like the sensation of warm stomach contents trickling down the back of your neck.
And I had just gotten out of the shower, too.