Having flown on Concorde 35 times, I can confirm that it has statistically been more prone to technical delays - off the top of my head I can think of five technical delays of more than 30 minutes and two where the standby aircraft had to be substituted. Both times the substitutions were for fuel leaks.
BA in fact operates a scheme where if the flight is delayed more than either 90 minutes or 2 hours - can't remember which - they will refund the fare paid by passengers. Obviously, the cost of doing this is pretty high, which is why I suspect they have the backup aircraft there - just in case!
The new interiors look great - I'm looking forward to seeing the 'lightwash' in action in the not too-distant future!