There's also things like "I was recording this for notes that I could review later." You can also determine if they have a reasonable expectation of privacy. They do not. This is how Wal-Mart records you without permission while you shop.

I've read a book or two on private investigator training because I want to take the test in my state at some point. One book I read talked about recording someone through their window and it was admissible in court. They didn't bother to draw the curtains and they did what they were doing in plain view of the window. Had hey drawn their curtains they would have an expectation of privacy.

I don't really think the two-party consent laws will defend them against this recording. No one in that room had an expectation of privacy.

Then the Trump Team needs this for the casework

It does if they admit to a crime or the planning of one.

If somebody is stupid enough to admit to a crime they did or planning, and there is evidence that leads to arrest, they are fucked. This isn't like TV. You don't need a warrant. If you are in the middle of a divorce you can record any phone call with your soon-to-be-ex as they are considered your wife still and they don't have reasonable expectation of privacy.

You only really need permission if you are archiving the conversation and there is no other reason to expect otherwise. If they are stupid enough to not agree to recording, and they admit they murdered somebody, they can still get arrested.

This would be completely admissible as evidence as long as they can identify who/what/where/when/why.

Evidence has to be presented before any proceeding otherwise its thrown out. Those gotcha games are the reason.