When you download Minecraft for Mac, you download an application file which you then place in your Applications folder. But that's just a wrapper for the "real" Minecraft binary files (a set of JAR files), which gets downloaded into your Application Support folder.
So when you delete and redownload the Minecraft application, you haven't done anything about the actual binaries already downloaded and being used. If these are corrupted (as they appear to be in your situation), they won't be fixed by redownloading the Minecraft application.
While "Force update" should do something about these files, you can do something about it yourself by manually deleting the downloaded JAR files.
To do this, you'll need to navigate to the path described in the error. In Finder, go to the Go menu and select Go to Folder... Type in the following:
~/Library/Application Support/minecraft
and click the Go button. Finder will open a new folder with a few subfolders, including one labeled bin. Throw the bin folder in the Trash and empty it.
Now go back into your Applications folder and open Minecraft. Minecraft will then redownload its binaries and the problem should be resolved.
I found the answer on the minecraft forums, so I'll repost it here.
http://www.minecraftforum.net/topic/36564-minecraft-on-osx-wont-open/
Thanks to
ahefner said: The bundle doesn't work because some unix file
permissions get screwed up as a result of distributing the app bundle
inside a zip file (versus, say, a .dmg). You can fix it from the
terminal using the chmod command as follows:
chmod +x ~/Downloads/Minecraft.app/Contents/MacOS/JavaApplicationStub
Modify the above command to reflect where you unzipped Minecraft at.
This will fix the bundle so that it opens when you click it.
Best Answer
Point finder to the Hard drive the install is stored on (Macintosh HD is a common name) and type minecraft.jar into the search. Then right click minecraft.jar and click "Show enclosing folder" and you should be in ~/path/minecraft/bin