Yes, a few important things to check:
- make sure windows 7 UAC is turned off (go to Control Panel -> User Accounts -> change User Account Control setting -> drag slider all the way to the bottom
- make sure your antivirus is disabled during the install as some AV's may interfere with the install process
- make sure the Mass Effect has access to the internet, if needed (can't remember if ME1 needed it but the DLC Bring Down the Sky definitely did)
- make sure to start the setup manually, so close down the autorun window, go to DVD drive, open the disc, r-click on Setup.exe and select Run as Administrator
and something I found out the hard way:
- if you're using an application called Process Explorer, shut it down before starting the installation (although this was only an issue during the DLC for me, it sounds like your symptoms are the same mine, so it's worth a shot)