I have developed this problem!
When I attempt to embed a video in K2 using the Embed tab the system throws this error and the page freezes.
I then have to delete the item
I have tried all the various solutions offered both here and in other places and cannot resolve it.
I can embed a video in the text area but I need the video to appear at the top of the item in the item view but not in the category view so I generally amend the php template accordingly

Hi,

Do you have any K2 plugins in the item form?

I do have "Insert code" from Sourcerer. I use it to insert Soundcloud items in the main text area.

Try to disable it for a while and see if that is causing the issue.

Tried it - no joy I'm afraid

Which other extensions are you using?
You can try the following.
Update K2, all other extensions and Joomla! to their latest versions if you haven't already. If it still fails, then try deactivating extensions one by one to see which one is causing the issue.

Problem solved!

I tried a completely clean installation with only K2 added and still got the same problem.
However I had noted that when I used the "Use online video service" tab I did not get the problem.

I then tried using the code that YouTube supplies on the normal YouTube Page in the Embed tab and it worked.

Because we generally render the video with "Modest Branding" "Related Video" and "Show Info" switches set I had always used the Youtube tool at developers.google to produce the code. (It saved typing the code myself when using an iPhone to manage sites on the fly at conferences)

I have only just realised they have made changes to that tool and it is producing code packed with blindingly obvious errors - if I had bothered to notice . Why do I assume Google get it right when I have ample evidence they get their code wrong fairly frequently?

It was a useful short cut which has in the end cost me hours.

Why does Google keep doing these things to us?

Thanks to both of you for your contribution.

Thank you for pointing the culprit David :)
Yes even Google can produce services with some 'issues'.