Not long ago (relatively) YouTube changed their video format from flash to WebM. I Think WebM is what is messing with your Tv file types.
I was having issues playing YouTube, and Netflix videos on my 7000 series Samsung. I went into my TV settings and checked my time zone and current time. Time zone was set incorrectly. Once I changed it to my local time zone I stopped having issues!
YouTube wirked fine until about mid December 2016 when it began giving me a blank gray screen. All else was fine. No other app problems. Nothing worked to fix my problem, so out came that Fire Stick again. I had plugged it into HDMI port 4, fiered it up, signed in and found the Youtube app on it. Now I eave it there on the Yutube app. On the Samsung Smart Hub that pops up on the bottom of my TV screen, I renamed the HDMI4 input port YOUTUBE and moved it near the things I use often. So, now I have a quick way to YouTube, just as if the app worked. Also, it is nice that the TV remote works with the Fire Stick so I don't need to use the Fire Stick remote. Since the Fire Stick sells for only $39.99, I consider this an acceptable solution after having spend about $1,000 on the TV.
The most likely issue is the web site changed and is no longer compatible with this Smart TV. As Smart TV makers don't update the browser to be more PC capable, when it dies, it dies.
~ Via cnet
all youtube videos say "playback error"
http://community.sony.com/t5/Internet-TV/all-youtube-videos-say-quot-playback-error-quot-kdl-47w802a/td-p/189397
Chances are, its in your TV setting since the changein video format.
WebM was adopted because it has a smaller file type signature.
I have downloaders that used to be able to handle flash and html video but can't handle webm file types.
WebM is an audiovisual media file format. It is primarily intended to offer a royalty-free alternative to use in the HTML5 video and the HTML5 audio tags. It has a sister project WebP for images. The development of the format is sponsored by Google, and the corresponding software is distributed under a BSD license.
What you probably need to do is find an app that reads webm files and download it to your TV browser.
This is easier said than done.
I have Gom Player which can be upgraded to read webm files.
You MIGHT be able to download a third party viewer like GOM and load the videos in that to display on your smart TV.
However, I only deal with a PC computer to view youtube videos and my browser (Waterfox) already reads webm files.
Not knowing the manufacturer of your Smart TV hampers my ability to advise you.
There are work arounds specifically for Samsung TVs and a few others.
http://streaminglearningcenter.com/blogs/try-hls-for-adaptive-delivery-to-smart-tvs.html
You might consider DASH as an upgrade.
Make sure that the latest system software (firmware) update has been installed. The latest software version available for the KDL47W802A is PKG3.710AAA.
Do a Refresh Internet Content.
1. Press the Home button.
2. Go to Settings.
3. Select Network.
4. Select Refresh Internet Content.
If you are still getting the error message after the refresh internet content, enter the IP address manually and change the Primary DNS to 8.8.8.8 and Secondary DNS to 8.8.4.4.
The Permanent Solution to Fix YouTube Responding Issues
Free HD Video Converter Factory is a functional YouTube video downloader
1. Free Download YouTube HD/1080p/4K/8K videos and play them on PC and portable devices offline without YouTube not working issue.
2. Convert YouTube to MP4, AVI, MKV, MP3, FLAC, etc. with original video/audio quality
3. Compress videos size to free up your storage devices for more videos
http://lifehacker.com/the-six-best-youtube-url-tricks-1422544868
If you want to get a local copy of a YouTube video, pwnyoutube.com can help. Just add "pwn" to the URL before "youtube" and you'll be taken to an external site with multiple options for download formats.
Hope this helped