Step 1:
To Watch Youtube Playlists in VLC we will be Using an addon, So Click here to Goto the Downloading Page of the VLC addon Called VLC Playlist Parser. Make sure you have Latest Version of VLC Running on your system.

Step 2:
Download the addon, Copy it and Paste it in Videos Installation folder which in most cases would be C:\Program Files\VideoLAN\VLC\lua\playlist.
Step 3:
Everything is done, Now Open VLC, Press CTRL+N Paste Video Playlist URL Which need to be Public. Click on Play and Enjoy all the Videos.

I Just Hope this tutorial on How to Watch Youtube Videos in VLC Media Player Helps all you Youtube Lovers.