I had the same problem, and thanks goes to Contrare for this fix that got it working on my comp.
I think this only works if you have Mapeditor installed in the right directory so make sure you haven't added any extra folders or such.
You need to open Terminal, which is in your Applications -->Utilities folder, or just search "terminal" in finder. Looks like a black box with >_ in the corner. Open it, and in the window type "cd /wyvern/mapedit" without the quotes. Now if you type "ls" (that's L S) you should get a list of the files in that directory. Now copy and paste this into the window..
java -cp mapedit.jar:jython.jar:skinlf.jar:xmlrpc.jar: .:wyvern -Dwyvern.home="/wyvern/mapedit/wyvern" wyvern.tools.editor.MapEdit
and hopefully it works :d