As Google and Sony can't solve their issues and release a YouTube stock app, we are made redundant to 'loopholes'. Anyway here's the tut:

1. Start the PS Vita browser and enter on the address bar:
http://oretube.blog99.fc2.com/blog-entry-75.html
2. Press on and hold PSVitaTubeDownloader until the 'open' dialog box appears
3. Then press 'open'
4. Then bookmark this page and name it 'Youtube downloader'.
5. Go to Youtube and select a video
6. Go into bookmarks and select 'Youtube downloader'
7. You should then see options to download the video in 1080/720/480p or what ever format the video is in, this should appear above the video box top left hand corner.
8. Select by pressing either 720p or 480p as 1080 doesn't playback.
9. Select and press save, you video will now download and be added automatically to your video folder.
10. Now play this video.

*I reccomend you on using your WiFi unless you have some sort of Unlimited Tehthering on your 3G Contract