Thanks for your help. I will try it later.Why do you need to open the InstallESD.dmg?
Just drag that file into your Disk Utility, and you can use the Restore tab to copy the image to a partition. 6GB should be great for the Mountain Lion installer.
You could also try using one of the apps that make the process easy. Lion Diskmaker works very nicely. I have several 8 GB flash drives, and have a couple dedicated for OS X installers. Lion Diskmaker (LDM) uses those, and erases them properly for best use with the Mountain Lion install. You can get that here: http://www.macupdate.com/app/mac/39701/lion-diskmaker
LDM will use a dedicated partition on a hard drive, or a USB flash key, or will also burn a DVD, whichever is what you want to do.
I suggest that burning a DVD is not worth your effort. Lion, and Mountain Lion installers are not optimized for booting from DVDs, and are really slow.
I think the best choice is an 8 GB flash key. My suggestion is to use a new flash drive just for the installer. You can find those everywhere for less than $10, and I have seen some for less than $6 ...
If that utility also doesn't like your Mountain Lion download - try restarting your Mac into Safe Boot mode (restart holding the Shift key), and try the same copy again.
If you still get the same error - then delete that download - it's likely just corrupted - and download again. You've already purchased the Mountain Lion install, so Apple doesn't charge you again.