There are lots of things you could do, from watching all of the videos since the one you last viewed, to a better way of editing playlists than the current one.
They should also make a way to preview videos, like hovering over the image of the video and you see a 15 or 30 second preview that you can choose from a part of the video. There should also be a way to instantly switch from computer to phone/tablet, just like chromecast.
If you just open up YouTube right now you can see how many links you can choose, there is way too much clutter on the front page.
YouTube has a great opportunity to distinguish themselves from traditional media, but they keep making design choices that prevent this. YouTube has become the leading video service because they created a platform that differentiated from traditional media, yet the current trajectory doesn't fit with that.
Chad Hurley is also one of the few notable alumni from the Technology Student Association, an organization I am a current member of that has not benefited from the recent increase in STEM funding. It is quite unfortunate, because they have a much more diverse offering than other stem organisations, even having an open source software competition!