Update: After several attempts, it looks like this may have been fixed in latest Chrome builds (per Paul Irish's comment below). That would suggest we will see this fixed in stable Chrome June-July 2016. Let's see ...
This is a known bug with the official Chromecast JavaScript library. Instead of failing silently, it dumps these error messages in all non-Chrome browsers as well as Chrome browsers where the Chromecast extension isn't present.
The Chromecast team have indicated they won't fix this bug.
If you are a developer shipping with this library, you can't do anything about it according to Chromecast team. You can only inform users to ignore the errors. (I believe Chromecast team is not entirely correct as the library could, at the least, avoid requesting the extension scipt if the browser is not Chrome. And I suspect it could be possible to suppress the error even if it is Chrome, but haven't tried anything.)
If you are a user annoyed by these console messages, you can switch to Chrome if not using it already. Within Chrome, either:
Update [Nov 13, 2014]: The problem has now been acknowledged by Google. A member of the Chromecast team seems to suggest the issue will be bypassed by a change the team is currently working on.
Update 2 [Feb 17, 2015]: The team claim there's nothing they can do to remove the error logs as it's a standard Chrome network error and they are still working on a long-term fix. Public comments on the bug tracker were closed with that update.
Update 3 [Dec 4, 2015]: This has finally been fixed! In the end, Chrome team simply added some code to block out this specific error. Hopefully some combination of devtools and extensions API will be improved in the future to make it possible to fix this kind of problem without patching the browser. Chrome Canary already has the patch, so it should roll out to all users around mid-January. Additionally, the team has confirmed the issue no longer affects other browsers as the SDK was updated to only activate if it's in Chrome.
Update 4 (April 30): Nope, not yet anyway. Thankfully Google's developer relations team are more aware than certain other stakeholders how badly this has affected developer experience. More whitelist updates have recently been made to clobber these log messages. Current status at top of the post.