A JAA Examiner may examine in any JAA State, but usually the candidate's home CAA will want a copy of the examiner's examiner authority (Odd, 'cos I thought we were all on the JAA database....) in order to issue, renew or revalidate a rating. The examiner can only sign for renewal/revalidations of ratings in a licence of his own home State.
As regards Commercial Air Transport, there is no reason why a TRE from one State should not be appointed to an AOC company of another state, but as Whopity says, the appointment must be acceptable to, and ratified by, the latter State's Flight Operations Inspectorate.