I have the same error message ('Network error -1001'). We have successfully had a network server software update running for 6 macs for years, but since we had to switch our IP address to the alternative ADSL2 line (Network settings), the network server software update stopped working.
I've researched Server Admin and logged into server to check settings and everything is as it should be.
It is not clear how you 'point' a mac to get it's software update from a network server.
On the server and other desktops in the office I can connect to the internet no problem, but software update fails with the same 'network error -1001 can't connect to the internet, check settings'. But we can and do have internet connection!
I have a similar problem. I have tried (multiple times) to download the latest ITunes software update and I keep getting this message: "The update Itunes can't be saved. A network error has occurred. (-3001). Make sure you can connect to the internet. Then try again. I am connected (I even downloaded a free song on ITunes to check.) Please - any suggestions???
OK, no one answered my query, but a good and clever friend suggested I just go to the apple download site and download the latest version of ITunes directly from the site. It worked.
I've been having the same issues. I realized it started ever since my employer put a proxy in safari which allowed us to connect to the internet. I just erased it and now my updates are fine.
check your network and hit advanced then search around there