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.
The Mac App Store does allow to resume a download, however things do not seem to work out always as expected - to be safe download it all in one piece.
Yesterday, I downloaded Mountain Lion from the Mac App Store - halted it - and resumed later without having restarted the Mac. The whole download started over. This is not the first time I have encountered it - therefore I do not take the pause/resume feature for granted.