I get the following errors when I try to install the Ubuntu SDK (ubuntu app development kit)

There's only one step:

sudo add-apt-repository ppa:ubuntu-sdk-team/ppa && sudo apt-get update && sudo apt-get dist-upgrade && sudo apt-get install ubuntu-sdk

Well, actually there are four, joined together with the && operator. You could run each step separately, but you can't divide them in the middle of a command, as you did.

The first two steps probably executed correctly and the third isn't strictly necessary. The errors you were getting on the fourth are probably due to the fact that the SDK team PPA is currently broken, as they just announced on the install page.

A day later: The problem with the PPA is apparently fixed. Try refreshing your package list (sudo apt-get update) and running the install step again.