As has been widely noted, Google has updated the mobile version of its YouTube site, and it no longer works for Vita owners, giving us the "Could not find the application" error. A shame, as the way pages worked on the Vita was very good for skipping adverts, and I had a long list of bookmarks for favourite songs and channels that I could play while working or relaxing.
If you have a shortcut, the fastest fix is to change it to
http://www.youtube.com/?app=desktop forcing the site to use desktop mode. Press the X on the blue bar to get rid of the annoying "We've redirected you..." message to free up some screen space.
UPDATED: Another fix for more recent issues is to go with http://www.youtube.com/?disable_polymer=true to turn off the new framework. However, in a strange twist the site doesn't work at all on my UK-setup OLED Vita, no matter what I do, but does work on my Vita slim setup for the US, so who knows what is really going on.
Other possible tips include clearing cookies and not using any existing bookmarks (a pain as I have dozens of songs saved like that!)
Even with that, the desktop site has can often be rather unhelpful with stuck-in-advert loops, reverting to the mobile site at random and other quirks. However, you can still play videos, through a semi-random fix.
Wait for an advert to play, then press back on the browser menu, press play again and your video should start. You might even get through a number of different videos before you end up in an advert loop again, depending on the channel you're watching.
That works for me mostly, your mileage may vary!
Looking at the YouTube update and engineering blog, there's no specific post about recent changes, and naturally no one to ask for a fix. Sony haven't updated the browser (Silk 3.2 according to a browsercheck, but really a Webkit-based version of NetFront) in many years. But NetFront is the Switch's choice of browser, so there must be reasonably modern updates for it, maybe there's some hope.
What we're really begging for is Sony to open up the Vita to allow third-party apps or an open source browser on there, but of course Sony won't do that! Then again, Sony finally updated a bit of the Vita store app for the first time in forever, so perhaps miracles do happen...
