Why can't my MacBook Air run Software Update?

One of the first things that I tried to do when I got my new MacBook Air out of the box was upgrade iTunes to 10.5 (through Software Update). It downloaded the files (four different updates in total), verified data, then started to write the files, at which point it stopped and said that it couldn’t complete the update.

Since then I’ve also downloaded the .dmg file for the iTunes upgrade and for the Lion 10.7.2 combo. My .dmgs can't be verified though; I get an invalid checksum error. I’ve downloaded them a bunch of times too just in case they were corrupted.

Then thinking that because it’s a new machine, I can just refresh the OS and start again, I tried the cmd+r boot and tried to just reinstall and it said:

Can’t install the additional components needed to install Mac OS X.

This is an ancient question (bumped by Community♦), but invalid checksum doesn't have anything to do with admin privileges, it is a bad download.

Since you tried multiple times you are either not getting the file despite the multiple tries, or the original file you are downloading is not complete.

I would look for another way to get the update.