Can I dismiss a Notification Center Alert using the mouse?
Yes! You can simply click and drag the alert off to the right and it will disappear. If you have a multi-touch input device such as a trackpad, you can also use two fingers and swipe it away to the right.

Additionally, you can temporarily move the notification by dragging it to the left:



It will stay there for a few seconds and then move back to its original position. This currently seems very buggy, but perhaps it'll work better with future updates.