The player will add a feature that was already available in Google Video: jump to any part of the video even if the video isn't fully downloaded.
For each video, you'll be able to see around ten related videos. You don't have to wait until the video ends to play a new one because they're available as thumbnails if you hover over the video. The effect is similar to the dock from Mac OS X. You can also click on the two arrows to go to the previous / next video.
The "menu" button gives you access to the embedding code or to the URL of the YouTube page that shows the video. If you click on the button, the video is smoothly minimized in the left corner and it continues to play.
Update. Here's the new player (thank you, TOMHTML):