So as the UK is part of the EU and citizens can move freely and live in other EU countries, do spouses of EU passport holders have any difficulties relocating to another EU country? So if a USC is married to a UK citizen and you decide to relocate to France for example, is there any issues getting the USC a residency or work permit? Anyone have any experience?

I'd be interested to know as well as I have wondered the same thing.

From what I know the non-EU citizen has to apply for residency/employment benefit in each country they want to live/work. How difficult that is depends on the laws implemented in these countries.

The USC would have to apply for an EEA family permit. I don't know all the details, but from what I've heard it's not too hard. Mostly a matter of applying and paying for it. Try googling EEA family permit and the country where you would want to move to.

My husband is Slovak and I the USC. When we moved to Poland, we had an agency take care of this for us. I think it took maximum 2 weeks. Wasn't difficult at all having the agency take care of it for us. Around $350 though.
Sorry I don't have more info for you.