Do Arduinos meet military standards?
It depends on the application. For something like a rechargeable torch, Arduino might exceed the specifications. For a weapons system, NEVER (and this is one of the specific prohibitions in the license agreement - see section 1.5 note: link currently broken). You also have to consider that there's literally thousands of armies in the world and they all have different standards. What might be acceptable to one might not be acceptable to another. Hamas uses rockets I wouldn't consider safe for anything, and they use them effectively - the Qassam rocket would never meet US military standards but it works great for Hamas.

US military standards are so complicated, nobody can answer this question for you. You're gonna need an army of lawyers to do that... here's a link to some documents to get started though...

Please note there are multiple standards which may apply to a given device. For example, you will see common off the shelf desktop computers (running Windows) used for some things in a military installation, but they could never be used to control a vehicle. Bottom line - you're gonna need a lawyer to navigate this. (You are better off selling your devices directly to soldiers, if you can live with that if it fails.)

http://www.dsp.dla.mil/ - Terrible site - get used to that if you want to deal with govs.

OH BTW... if you want to use Arduino to prototype something, and you plan to remove "Arduino" later, running straight from the ATMega - that's the whole point of Arduino! It is a prototyping system, not intended to be used wholly in products. Arduino is very little more than a break-out board for the ATMega processor, a robust (kinda) power supply, and a runtime environment in C++.