That being said here are some improvements that you might want to consider:
1. I almost dismissed this as another thing that I'll never use until I found that search bar on the top right. You want to make sure it's visible at first glance.
2. Allow me to drag the volume slider.
3. The button next to the cross/remove is not very intuitive. Took a good 10 seconds before realizing I could drag it. Make tooltip available everywhere.
4. The default video width can be bigger.
5. If a video from the search result is playing, change its play button to a pause so I know that when I scan that list.
6. If there is one thing I'd want to carry from youtube here is recommendations. Sometimes I might not know what to search for. So have a tabbed view between search results & recommendations.
7. You'll probably come to this anyway but I'd like to create an account so I can save my playlists.
Best of luck.
Edit: PS: Just realized I could use a next/previous button.