Open normal Minecraft launcher and login with your username and password as normal. Now open another Minecraft launcher in a new window and login with the same username and password. Leaving both windows open, go back to the first Minecraft Window and try to join a server and the screen will appear with 'Failed To Login: Bad Login' but you are able to join a server in the second Minecraft Window.

This might not be a bug but I'm reporting it as I found it by accident and thought that some people might want to play on a server in one window while playing on a server on the other, maybe to copy a design or something, but it's not possible to do so.