This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
I don't think there is an easy way to find that out directly from a war file. However, you could look inside the war file for *.class files (in the WEB-INF/classes directory). This blog post explains how you can get the version number of a class file using javap (a tool that is included with the JDK). The version number tells you for which Java version the class file is compiled; for example 50 is Java 6, 49 is Java 5.