I'm sorry but The Producers is probably one of the stagiest musical films in years. It felt like it was a play at points, the performances were a little too over-the-top for the screen, and actors singing directly to the camera didn't really seem to work. So Stroman does not deserve any sort of directing nominations, look at what Rob Marshall did with Chicago, that is a good director.
As far as nominations for Rent or The Producers, I doubt either will get any major nods just because of the films with major buzz that have been coming out these past three months or so. I believe from Rent, the only one that has the slightest chance to get a nod is Rosario Dawson. From The Producers, I doubt anyone will get a nomination, perhaps Lane or Thurman, hopefully not Ferrel, I still can't get over the fact he got a Golden Globe nod.
"Some people can thrive and bloom living life in a living room, that's perfect for some people of one hundred and five. But I at least gotta try, when I think of all the sights that I gotta see, all the places I gotta play, all the things that I gotta be at"