I would add Carlos Castillo's other shop. It is much less trendy than Man 1924. It is called Denis and is just off of Serrano. They carry Drake's, Simonnot-Godard, Alden, though I can't say who makes their clothes (mostly unstructured jackets).
Just around the corner on Serrano itself is Best, which is partially owned by Jaime Gallo, who most tailors here say is the best in town and whose workshop is not too far away. The wares there can be a bit on the dowdy side, but you will find at least a few Drakes ties for 40% off retail.
Of the three Carmina shops, the one on Serrano is a little envelope of a shop but worth checking out. The other two, one a block away from Serrano on Coello and the other on Gran Via are larger and staffed with people who have passable English (the Gran Via shop less so than Coello).
As for Scalpers, I don't know what to say except beware any place that washes its shop in cheap cologne.
I would definitely check out the Chagall exhibit, and of course spend at least an hour at the Prado, even if just to sit with Goya's late work.
Though it is approaching summer, make sure to have Cocido when in Madrid, especially if you've never had it; there are several traditional joints, but I can't seem to think of one right now.
Also consider day-tripping to Segovia, where they will roast you a piglet small enough to fit on a plate feet to snout.
Burgos is a very good shop, and though they do have some RTW shirts, they are known for their bespoke service, which is excellent (I started using them when I moved here), but unless you are in town fifteen or sixteen days so they can see the shirt on you, I wouldn't have one made while here. That is to say, it can be a bit of work getting fit right with them, though the craftsmanship is quite special.
A few last opinions: the shoe outlets in Chueca, i'm sorry to say, are not very good; Loewe is terribly overpriced and, forgive me, riding on the history of its name; and both times I've been in Meermin i've noticed more than a few seconds on display as firsts. I don't believe the occurrences accidents, they just seam poorly made.