Just when all of these dumb things are happening, whom should come rocketing down the chimney but the sexy restorative balm we call the Doctor, flopping around with his hair and all. He thought it would be fun to enter the scene Santa Claus-style, and then babble at them for awhile in some sub-par Buffy ergot about the "chimneyness" and the "bored now" and whatever else Stephen Moffatt probably thinks is clever. There's a great deal of talk to the poor people about Father Christmas and Frank Sinatra's hunting lodge and Albert Einstein, with whom apparently the Doctor and Marilyn Monroe had a threesome. In the future of the past, which has not yet happened. Or else the threesome was with Father Christmas and Albert Einstein, which makes more sense and is easily four times as annoying to think about.
The Doctor starts in messing about with Scrooge's console, having not stopped talking and showing no signs of slowing down, and figures out that it "controls the sky," which as you rightfully point out means nothing. Technically, what it controls is the clouds, which technically are made of tiny particles of ice, which contain fish and also sharks. At which point, I think, we've officially hit the record number of random pointless things shoved into a given episode that was first established with the abominable "Beast Below." Difference being this episode is fairly great, and of course also taking into account that Christmas episodes generally have sucked. But then, much less far to fall these days, I suppose.
Scrooge assures the Doctor that the lady on ice is nobody important and the Doctor cocks an eyebrow. "Blimey, that's amazing. Do you know, in 900 years of time and space, I've never met anyone who wasn't important before." Somehow, thanks to Matt Smith, it comes off as generally appealing and not a condescending load. He fiddles with the control for a bit before Scrooge explains that it's isomorphic and will only respond to he himself: "The skies of this entire world are mine. My family tamed them, and now I own them."
Cue the Doctor to be insufferable again -- "Tamed the sky? What does that mean?" -- and they talk about how Scrooge is very, very important and the Doctor doesn't know who he is, and then before you know it he's threatened Scrooge's very life if they don't save Amy from her sex boat. Finally the Doctor leaves, and Scrooge tosses the Cratchits out as well, with glorious aplomb: "And next time, try and find me some funny poor people!"