This might actually be _two_ bugs.

1) Running 'Image > Properties...' or 'Analyze > Set Scale...' to change the units and scale will change only the units for x, *not* the units for y and z directions.
The same problem apparently occurs when saving a virtual stack (with micron calibration) to a tiff stack: the resulting file will have microns in x and pixels in y and z.

2) As a consequence, when you save such a "mis-scaled" image and read it with Bio-Formats Importer, the stack trace pasted below is thrown. Unfortunately, this breaks any use of the Grid/Collection Stitching plugin because it exclusively uses Bio-Formats to open even "Standard ImageJ" tiff files.
I suggest that the Bio-Formats Importer should be a bit more forgiving and issue a warning only, instead of throwing an exception here.

This macro code illustrates both issues:

// ******************************************************
  tmp = getDirectory("temp");
  file_name = "calibration_bug.tif"

  newImage("Calibration_test", "8-bit black", 100, 100, 20);
  run("Properties...", "channels=1 slices=20 frames=1 unit=um pixel_width=0.8 pixel_height=0.8 voxel_depth=0.8");
  Stack.getUnits(x, y, z, t, val);
  print("Units: x=" + x + " y=" + y + " z=" + z + " time=" + t + " value=" + val);

  saveAs("Tiff", tmp + file_name);
  run("Bio-Formats Importer", "open=" + tmp + file_name +" color_mode=Default view=Hyperstack stack_order=XYCZT");
// ******************************************************


Here's the stack trace:
(Fiji Is Just) ImageJ 2.0.0-rc-30/1.49u; Java 1.6.0_24 [64-bit]; Windows 7 6.1; 46MB of 98221MB (<1%)
 
java.lang.NullPointerException
	at loci.plugins.in.Calibrator.applyCalibration(Calibrator.java:71)
	at loci.plugins.in.ImagePlusReader.readImage(ImagePlusReader.java:307)
	at loci.plugins.in.ImagePlusReader.readImages(ImagePlusReader.java:238)
	at loci.plugins.in.ImagePlusReader.readImages(ImagePlusReader.java:216)
	at loci.plugins.in.ImagePlusReader.openImagePlus(ImagePlusReader.java:111)
	at loci.plugins.in.Importer.readPixels(Importer.java:146)
	at loci.plugins.in.Importer.run(Importer.java:85)
	at loci.plugins.LociImporter.run(LociImporter.java:78)
	at ij.IJ.runUserPlugIn(IJ.java:199)
	at ij.IJ.runPlugIn(IJ.java:163)
	at ij.Executer.runCommand(Executer.java:132)
	at ij.Executer.run(Executer.java:62)
	at ij.IJ.run(IJ.java:279)
	at ij.macro.Functions.doRun(Functions.java:597)
	at ij.macro.Functions.doFunction(Functions.java:95)
	at ij.macro.Interpreter.doStatement(Interpreter.java:227)
	at ij.macro.Interpreter.doStatements(Interpreter.java:215)
	at ij.macro.Interpreter.run(Interpreter.java:112)
	at ij.macro.Interpreter.run(Interpreter.java:82)
	at ij.macro.Interpreter.run(Interpreter.java:93)
	at ij.plugin.Macro_Runner.runMacro(Macro_Runner.java:153)
	at ij.IJ.runMacro(IJ.java:116)
	at ij.IJ.runMacro(IJ.java:105)
	at net.imagej.legacy.IJ1Helper.runMacro(IJ1Helper.java:857)
	at net.imagej.legacy.plugin.IJ1MacroEngine.eval(IJ1MacroEngine.java:116)
	at net.imagej.legacy.plugin.IJ1MacroEngine.eval(IJ1MacroEngine.java:163)
	at org.scijava.script.ScriptModule.run(ScriptModule.java:175)
	at org.scijava.module.ModuleRunner.run(ModuleRunner.java:167)
	at org.scijava.module.ModuleRunner.call(ModuleRunner.java:126)
	at org.scijava.module.ModuleRunner.call(ModuleRunner.java:65)
	at org.scijava.thread.DefaultThreadService$2.call(DefaultThreadService.java:181)
	at java.util.concurrent.FutureTask$Sync.innerRun(FutureTask.java:303)
	at java.util.concurrent.FutureTask.run(FutureTask.java:138)
	at java.util.concurrent.ThreadPoolExecutor$Worker.runTask(ThreadPoolExecutor.java:886)
	at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:908)
	at java.lang.Thread.run(Thread.java:662)

Information about your version of Java:

  os.arch => amd64
  os.name => Windows 7
  os.version => 6.1
  java.version => 1.6.0_24
  java.vendor => Sun Microsystems Inc.
  java.runtime.name => Java(TM) SE Runtime Environment
  java.runtime.version => 1.6.0_24-b07
  java.vm.name => Java HotSpot(TM) 64-Bit Server VM
  java.vm.version => 19.1-b02
  java.vm.vendor => Sun Microsystems Inc.
  java.vm.info => mixed mode
  java.awt.graphicsenv => sun.awt.Win32GraphicsEnvironment
  java.specification.name => Java Platform API Specification
  java.specification.version => 1.6
  sun.cpu.endian => little
  sun.desktop => windows
  file.separator => \

The up-to-date check says: REMIND_LATER

Information relevant to JAVA_HOME related problems:

  JAVA_HOME is set to: C:\UTILIT~1\FIJI-D~1.APP/java/win64/jdk1.6.0_24//jre
  imagej.dir => C:\UTILIT~1\FIJI-D~1.APP

Information about the version of each plugin:

Activated update sites:
ImageJ: http://update.imagej.net/ (last check:20150618000647)
Fiji: http://fiji.sc/update/ (last check:20150617220654)