I observed inconsistent behaviour of the window manager in Fiji.
When opening a few sample images and closing one or more of them, e.g.

run("Blobs (25K)");
run("Boats (356K)");
run("Clown (14K)");
close();

the entries in the 'Window' menu do not correspond to the opened images. In my example, the window menu contains

  blobs.gif 63K
  clown.jpg 248K

although the open images are blobs.gif and boats.gif.

Closing all images results on one entry being left over in the window menu.
Also, the appearance of tick marks in front of the currently active window is inconsistent.

Information about your version of Java:

  os.arch => x86_64
  os.name => Mac OS X
  os.version => 10.9.3
  java.version => 1.6.0_65
  java.vendor => Apple Inc.
  java.runtime.name => Java(TM) SE Runtime Environment
  java.runtime.version => 1.6.0_65-b14-462-11M4609
  java.vm.name => Java HotSpot(TM) 64-Bit Server VM
  java.vm.version => 20.65-b04-462
  java.vm.vendor => Apple Inc.
  java.vm.info => mixed mode
  java.awt.graphicsenv => apple.awt.CGraphicsEnvironment
  java.specification.name => Java Platform API Specification
  java.specification.version => 1.6
  sun.cpu.endian => little
  sun.desktop => null
  file.separator => /

The up-to-date check says: REMIND_LATER

Information relevant to JAVA_HOME related problems:

  JAVA_HOME is set to: null
  imagej.dir => /Users/eglinger/Fiji-debug/Fiji.app

Information about the version of each plugin:

Activated update sites:
ImageJ: http://update.imagej.net/ (last check:20140610234546)
Fiji: http://fiji.sc/update/ (last check:20140611000938)