Best to use an unscented detergent, in addition to the vinegar, for laundering, in order to remove the oil buildup. I've never used vinegar+water as a de facto room spray before--the most common recommendation is to leave it in a bowl (up out of reach!) where it can absorb odors. Wiping down the cage with it is a great way to clean!
You can leave the baking soda on the carpet but only while the ferrets are kept out of the room. The main concern is that they would inhale it. Otherwise it's a very nontoxic way to freshen carpets.
I use 50/50 vinegar/water mix in a spray bottle to spot clean cages. And no, the baking soda cannot be left on the carpet with them running about on it. I agree with unclejoe- "sweep" the baking soda into the carpet, then vacuum thoroughly after about an hour.
Ferrets: Contessa Kitties: Watson, Oskar DIP Sinnead, Vincent, Boris, Zeus and Athena, Willow, Mr. Frodo, Indie, Lucrezia, Judge, Odin, Miss Emily, Suki, Cody, Aristotle, Butterscotch, Frankenfurter. RIP Herne, Ligeia, and Mr. Stubbs