What issues do you need to check for deploying a java application on linux?

Ensure that any third part JAR files you use (such as SWT) have the appropriate platform-dependent version. While you said "without any specific platform dependencies", platform-specific behavior can sometimes be hidden.

Also:

1. File paths (do you have paths such as C:\Program Files?)
2. File paths (do you use '/' or '\' or do you use the appropriate constant File.pathSeparator?)
3. How do you locate important directories such as the user's home directory?
4. If you're opening sockets below port 1024, will you be the root user in UNIX?
5. Will you be using the Sun JVM, gcj, or some other JVM? Will differences in implementation or performance affect your application?
6. Check the JVM release notes (e.g., for J2SE 5 or Java SE 6) for mention of bugs or other behavior differences on your platforms of choice.

You'll almost certainly want to set

-Djava.awt.headless=true

in case any libraries try to do any font rendering, image manipulation, or anything else that touches Swing, AWT or ImageIO