YouTube – How to Export a YouTube Playlist

As far as I am aware, there's no built in way to do this on Youtube.

You could of course use the Youtube API to easily get all of your playlists in xml using the following:

https://gdata.youtube.com/feeds/api/users/[YOUR_USER_NAME]/playlists?v=2

Example: https://gdata.youtube.com/feeds/api/users/oisinorion/playlists?v=2

That xml file will have the unique IDs for each of your playlists, which you can then use to get the details for each playlist, including Video URLs and titles. The following API call will again give you an xml file:

https://gdata.youtube.com/feeds/api/playlists/[UNIQUE_ID]?v=2

Example: https://gdata.youtube.com/feeds/api/playlists/D5F03C2BE1AA3E7E?v=2

Working with those XML files manually would be a nightmare however. It would be best to create a small web app (if you know a bit of web programming) to pull out and present the relevant info from those XML files.

You can read more about the API here: https://developers.google.com/youtube/2.0/developers_guide_protocol_playlists

In the old YouTube, if I'm watching a video from my playlist, I could delete

YouTube new additions allow you to Delete videos (for non-autogenerated playlist and unless they have been deleted already).

and rearrange videos in that playlist using the bar at the bottom of the page

This functionality is still lost in the playlist (or at least I wasn't able to "drag" videos around)