What is this Windows Vista/7 window doing on the wall in episode 3 of Re-Kan?
It's a screenshot from LMTOOLS by Flexera Software. As it's a tool for working with a software licencing management server, I think you're right and it's out place on the wall of an average Japanese highschool.  It hard to see such a specialized tool being the subject of instruction, and the screenshot alone stuck to a wall wouldn't serve any purpose.

I'm guessing the screenshot was grabbed from the Internet somewhere. Like this one I found on as part of a FAQ entry on using the tool: