I tried several Accounts on my computer with the newest launcher for 1.6 and it doesn't let me log in.
Error: "Could not login: Invalid credentials"
I also tried it several times to make sure that I didn't type the wrong password.
And yes I'm using my e-mail to log in.

Mojang page: Success
Minecraft page: Success
Old Launcher for MC 1.5.x: Success
New Launcher: Failed

There is also this thread I found on minecraftforum.net
http://www.minecraftforum.net/topic/1856302-invalid-login-with-any-account/