2010 Dodge 3500 with just under 10,000 miles. By 2011, the paint had flaked off of the back of the differential housing, and, of course, it is covered with rust. Dealer says it is normal. Is it?

 

the paint they use on the differentials is probably the cheapest they can get .and they don't prepare for paint!
if you want it better then clean the rust off and paint with some good engine paint.
after i did mine it lasted for years before the rust started to show again

 

And you're in Arizona too. You should see what they look like up here. I bought a case of CRC Marine Corrosion Inhibitor and did the frame and axles on my 2012 2500 4x4. This stuff is designed to resist rust and corrosion on salt water marine engines and I can't recommend it enough. It goes on clear and has a slightly yellow tint that you can't see on a black frame or axles anyway. It doesn't flake like so called rustproofing and it looks completely natural when it dries...in fact it makes your frame and axles look new especially if applied before the rust starts. My truck looks new underneath and it has a plow on it. Even if you have some scale or rust it pretty much stops any progression. I put this stuff on every new truck I buy and all the old ones too. Ok to use on brake lines, electrical connections etc. Google it...wide range of prices online.