JOSM gave me a message saying my version of Java soon won’t be supported. I assumed I had Java 6 without realizing it, and updated to Java 7 version 25. Java’s verifier says I have the latest version, but I still get the outdated version message in JOSM. Is this a bug, or is the message not updating properly?
What operating system are you using?
Try running this from a command line, and see what it says:
java -version
If using Windows, check Add/Remove Programs, and see what it lists for Java. If there are old versions listed, then its a good idea to uninstall them.
I’m using Windows 7 Home Premium x64.
Programs and Features (:P) lists two things:
-Java 7 Update 25
-Java™ 6 Update 17 (64-bit)
This is odd, because the verifier tool on Java.com said there were no old versions. Also, why is the outdated one more detailed?
Running “java -version” gave me this:
java version "1.6.0_17"
Java(TM) SE Runtime Environment (build 1.6.0_17-b04)
Java HotSpot(TM) 64-Bit Server VM (build 14.3-b01, mixed mode)
I’m assuming, based on what it says in Programs and Features, that “1.6.0_17” means Java 6 version 17. 
Should uninstalling the older one fix this?
Yes, try to uninstall Java6 and keep the 7 version.