YS, your post is not quite invisible.
I'm going to resist reading. I want to wait until the book. Of course that's completely unrealistic... I hope I can wait a week at least.
Edit: Okay... I waited all of ten minutes before reading it. So sue me!
ALERT!
The rest of my post will contain major spoilers... Beware!
This is your final caveat... I will not make the text invisible... spoilers will be rampant.
Kill the boy. My first thought was that Jon needs to mature quickly in his decision making. He's crossed his rubicon, there are no room for delusions and fancies. So Jon desires that both he and Sam grow up. The apostle Paul wrote to the effect of maturity... When I was a child, I used to speak as a child, think as a child, reason as a child; when I became a man, I did away with childish things.
But after Jon's rememberance of Bran and Tommen yet before the explanation from Aemon, I thought mayhaps kill the boy meant kill Tommen or I thought mayhaps it meant that Jon was privy to Cersei's plan to kill him.
Anyway it seems that Jon knows that as much as he writes to the Iron Throne or professes neutrality he will not ever be at peace with the Lannisters. Just as Stannis is in a death struggle with Tommen, Jon will have to outlive Cersei to cease hostilities with House Lannister.
I wondered about the method of Janos' execution. Yet upon reading YS' explanation it makes perfect sense. Janos and Alliser and their supporters learned first hand that Jon's memory, decisiveness, and power are precise. Janos threatened Jon with hanging. Jon hung Janos.
I'm not an expert in capital punishment. I know that during a hanging the neck must be broken from the fall or the condemned will slowly suffocate. The distance for the fall depends upon the weight of the condemned. I'm not sure but I think the distance is between three to five feet. There was an instance in the American Old West where a bandit was dropped from ten feet or more and the suddeness of the stop decapitated him. I'm certain a drop of 100 feet would decapitate Janos Slynt.
But I'm not sorry to see that slimy, ferret faced, back stabbing toad die.