Sherlock has his phone (looks to me like that at least) in his hands there, hiding it cleverly in his coat sleeve most of the times.

Why? That leads to my idea related to quote above from Steven Moffat.

I am referring to the conversation between Sherlock and Jim on the roof. Sherlock is doing something out of character there: He’s asking questions, he seems confused. But only that much to not make Jim suspicious.

Sherlock: But the rhythm … 

Jim: Partita no. 1, thank you, Johann Sebastian Bach

Sherlock: But then how did you …?

And then Jim explains his entire plan how he broke in several important buildings at once. It’s not the only time in that conversation where Sherlock acts like the “dumber one” of both, of course not too bluntly so Jim doesn’t realize what’s going on.

Why does Sherlock act like he’s lost and hasn’t figured out Jim’s entire plan? So he can record what Jim is saying (in sense of a confession) on his phone, which he has in his hand/coat sleeve.

When you watch the scene again, Sherlock steps to the edge of the roof, till to that point he was acting. Then he starts laughing, cause he feels like he has won. The most important parts he probably has recorded. So he steps back down again. Now he’s back to his “normal self”. I feel like you can see it in his attitude even (comparing 2nd screenshot with 3rd)

Later, when he’s on the phone with John, Sherlock says: “This is my note.”

Before he jumps of the building, he throws the phone away, to leave it on the roof. 

Hmm, these are my thoughts to the scene so far.

UPDATE: Here’s now my follow-up post :)