After I set up Apple Mail to use my Gmail account, I had a couple things I was still having to go to the Gmail web interface for. One of those was managing multiple labels for a particular message. Since that time, I did some experimenting and have figured out how to manage the labels with Apple Mail. I'm pretty sure you could use any mail client that supports IMAP and you'd have the same results.
Here is how you can manage multiple labels for a message:
Dragging a message to a folder is the same as adding a label. You can add an additional label to a message by copying the message to the 2nd folder. Note that if you drag a message from one folder to another, the default operation is to move it. You can use command-c, command-v to copy/paste, or you can right click the message and choose "copy to" in order to apply the 2nd label.
When you view your mail through the web interface, you'll see the same message with two labels instead of two different messages even though intuitively, you'd think that copying creates another message.
Removing a label is the same as I reported in my earlier post. Just drag your message to the "All Mail" folder. A copy will still appear in the other label folders.
I noticed a quirk too. If you have a message in more than one folder and you delete it, it disappears from all the folders. The funny thing is, if you drag it back to a folder, it re-appears in all the other folders it was previously in. I guess in this way if you make a mistake, it is easy to undo.
That's all. Enjoy.