I remember talking to a Concorde pilot about a previous occasion. If my memory serves me right this was an occasions when the aircraft lost part of the top of the tail in the cruise. The first the crew knew was vibration. They came back to subsonic and during deceleration the vibration largely ceased. When they put the power back on to maintain subsonic cruise it came back. Experimentation discovered that throttling one engine up (forget which) seemed to provoke vibration so they shut it down. On finals they had some problems with control (the comment "had to give the rudder a real boot to straighten it up" comes to mind) but put it down to the asymetric engine condtion.
As with this latest occasion the loss of rudder section was pointed out by tower on landing.