He is still in the face-off circle when he takes a "peak" (which more looks like he is looking at the forechecker than behind him), there is lots of ground to cover before he reaches the puck. Point still being, he is responsible for where he puts the puck, he can't just assume, which is what he did. If you drop the puck behind your own net, you better make sure someone is there, and more importantly, a member from the other team isn't.
If Cleary went across in front of the net, you drop it, if he goes behind, you move it forward. Cleary went by Phaneuf and toward the back of the net before Jake dropped it. I am no Phaneuf fan and he was slow to react, but if you put a puck on an opponents stick without looking just because you thought a teammate would be there. It's on you.
You've touch upon some of what plagues his game - it's those little details. Babs believes these details are fixable. Giddy-up.