Do tell, that's news to me, what happened with Billy and Patrick?

There were a couple of interesting stories regarding this episode:

https://columbophile.com/2023/06/04/the-mystery-and-murder-of-murder-with-too-many-notes/

And this, in which (near the end) the story of a drunk Billy Connolly gets publicly shamed by Patrick McGoohan.
https://columbophile.com/2023/04/30/columbo-episode-review-murder-with-too-many-notes/

I may have come across more details of the conflict on the set between these two, but I can't recall exactly where.

There might be some on YouTube, maybe among general Columbo outtakes?