They have an add-on for Toolset compatibility, are you using it?
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I can see from our internal tickets that this same error was reported a year ago, and that we had some interactions with the plugin author that ultimately proved fruitless.
The plugin creates duplicate posts on other sites on a network, but isn't doing it correctly with Types custom fields.
We'd be happy to try again to help the Broadcast plugin author identify what's required. I suggest you file a support ticket with them, where you can invite them to contact the Types developer jan.s@onthegosystems.com for assistance.
I've updated our internal tickets to link them to this thread.
From the internal tickets it looks like there is some email communication between the developer of Broadcast and of Types, so hopefully that means a solution can be found.
I'll leave this escalated and update you if I see any news.