Is it really so easy for a non-citizen of one EU country to get permanent residence in another EU country?  I would think there are all kinds of residency issues...

No, there really are no residency issues.  Citizens of any EU country can live and work in any other EU country with no visas etc.,  needed.  Just pack up and go.  The aim was to make it as easy to work across the EU as it is across the USA. 

Of course, the languages are a significant barrier. 

But from the POV of immigration/residency, there are no barriers within the EU for any EU citizen.  I am Scottish too.  I spent three years working in Nice during my career, no visa or permits were necessary.  Fortunately we speak French so no language barrier either. 

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