Loss of airspeed information does not present an imminent danger to the aircraft - all transport airplanes (and I suppose military aircraft as well) carry multiple redundant Air Data sensor suites that 'should' always provide the pilots with accurate and reliable air data (such as altitude, Mach number and dynamic pressure i.e. indicated airspeed). Even if these sources fail the pilots are/should be able to fly the aircraft without this information - the combination of pitch and power necessary to fly a certain speed at a certain altitude is something that one learns naturally when getting acquainted to a new aircraft. I don't know of any instance where the Concorde suffered from a loss of air data resulting in a serious problem - there are only very few incidents in history where this was the case on other aircraft (where factors such as Crew Resource Management and Situational Awareness also played a role). All the talk about the 'faulty' pitot probes could so far not explain what happened to that A330 over the Atlantic, even the investigators unfortunately don't know enough at the moment to make more than an educated guess about what happened during that flight...