Can I resume an interrupted download of Mac OS X Mountain Lion? I have a slow internet connection. I want to download Mountain Lion (Mac OS X 10.8) from the Mac App Store and resume the download if it gets interrupted because of my internet connection.

Does the Mac App Store allow resuming broken downloads?
Yes - the App store handles interrupted purchases without intervention in most cases. There is a support article if you want to nudge things or it manages to wedge itself.

You don't have to let the download complete on iOS or Mac OS X and can control things on the Mac side of the store much better than on iOS.