Is it possible to burn a DVD (or usb bootable drive) out of the Mountain Lion app store install?
Yes it's possible, you can find a couple of useful guides for the steps required. Here is one from Macworld.
The main points are to do it before installing Mountain Lion as the installer will delete the install files, and use the disk image in the application package as the source for your USB key or DVD.
The USB key will generally give you better performance if you need to reinstall OS X later.
As has been said, it IS possible. Easiest way to do it is with this tool:
Took me all of about five minutes to get it taken care of with a run-of-the-mill 8GB flash drive.
As tRehak pointed out, though: Don't install Mountain Lion until you've made the drive/burned the DVD. Otherwise, you'll have to re-download the installer all over again.