If I have downloaded Install OSX Mountain Lion application file from the Appstore, I can use it as an installer on multiple machines.
Any idea for how many machines will this be valid? How apple verifies a valid install?
I wish I could give better answer, but I can't fully resolve the problem of Apple's differentiation between iTunes Store, Mac App Store, App Store and iBook Store.
If you read the following official document, Apple only talks about the iTunes Store when it comes to licensing and iTunes-authorized computers.
My understanding is that the same rules apply to all purchases made in any of these stores because the receipt via Email is always from email@example.com - no matter if the purchase is an iOS App, a Mac App, or a a song...
Since you purchased Mountain Lion in the Mac App Store, it's an iTunes product which you can install on up to five Macs at the same time. I've installed Mountain Lion using the same self-made USB installer on three different Macs without problems.
You can install Mountain Lion on any Mac you own:
"Authorized" just means that you have to sign into the Mac App Store with the Apple ID you used to purchase Mountain Lion.
The instructions actually tell you to re-download the installer on each machine, but it works fine if you simply copy the installer from one machine to another (which makes sense since it's the same file either way). Maybe they want you to re-download it on each machine so they can track how many times you download/install it on your account? But they clearly state that you can install it on "all" of your machines, which implies there's no limit.