As a new mac user, I have little experience but heard all good things about mac. (but very good at pc)
I however encountered this same issue as most of the downloaded dmg files are "corrupted" in my first two days. Read a few posts here and in other forums, here is what i did:
1. Tried to use "disk utility" to find error and repair the partition and disk. As folks are saying most likely it can be a bad disk or bad memory, i.e: hardware problem. I was thinking i just got bad luck as it is a brand new mac air.
Well, it did find one error on disk: a group value is wrong, should be 0 but is now 80. fixed it.. Tried to download the same dmg files(office for mac trial, and os upgrade). still corrupted.
2. Saw someone mention that could be wireless router problem. As I have PCs and Ipad and other devices running on the same router and internet, I do not think that is the case. But i did(now as i look back) encountered a few werid error when i used my pc to download some microsoft updates too. And I may have blaimed win8 wrongly for its suck app store(*_^).
3. Called apple support, the junior guy can not fix it then passed me to the senior guy.Here is how we fixed it (but I strongly feel also because I reset my cable modem as well during the fix):
Reboot the mac, get into the restore mode, from there use the disk utility app to find and repair the error i mentioned above in 1.
Reboot, although I can not see any updates of the OS in the apple store no more, i can still go to the website get the dmg downloaded and now, bingo... it works...
And again, now putting all these together, I think i may also hooked up with a bad modem on the time warner cable side for a few days ut as i most tiem do not download any new software, i never paid attention to it... this may explained why we can not get youtube play videos smoothly....
and anyway, except now the new os drain my battery like crazy..(i only get 3.5hours out of the 7hours claimed), this machine works like a chime....i really like the smart mouse pad.... love it.
Oki, hope this may be helpful for someone...
And apple, please fix the os and show me the 7 hours battery....