Yesterday I purchased the upgrade to Lightroom 4. I was using Lightroom 2. I downloaded the .dmg file successfully, but when I tried opening it, I got an error message saying there was an error with the .pkg file. I tried downloading the .dmg install file from the Adobe website 3 separate times. Each time it downloaded successfully, but I still received the same .pkg error message.
I assume you're on a Mac. You need to be running OSX 10.6.8 or higher on a 64-bit machine to run LR4.