According to the NTSB report on the 1973 crash of Pan Am Flight 160, the 707-300C1 has lateral controllability characteristics ranging from “minimal” to “none” if the flaps and spoilers are extended with the yaw damper inoperative:
Performance data for the Boeing 707-321C show that lateral control capability may be extremely limited, if not impossible, with an inoperative yaw damper, extended spoilers, and lowered flaps. [NTSB-AAR-74-16, p. 31 (marked as 29).]
On most aircraft, the yaw damper, although useful, can still be rendered inoperative in all flight regimes without causing the aircraft to become uncontrollable. Which makes sense - of the two main uses for the yaw damper (minimising Dutch roll and helping to counter adverse yaw), the first is of little consequence at the low altitudes where the flaps and spoilers are most likely to be deployed simultaneously (as Dutch roll is strongly damped out by the thick, dense low-altitude air), and is not generally a threat to controllability even when weakly damped at high altitude3 (although it excels at making the aircraft’s occupants airsick), while adverse yaw can be countered just as well by manual rudder inputs (something every jetliner pilot will have long since learned how to do, manual rudder usage being necessary for making coordinated turns in the small general-aviation planes pilots first learn to fly in) as by the yaw damper. Granted, the very high induced drag generated by flap and spoiler deployment (mostly the latter) would considerably aggravate the aircraft’s adverse-yaw tendency,4 but, assuming that the 707’s rudder was adequately sized to begin with, the aircraft should still remain completely controllable with the proper manual rudder inputs.
Indeed, if the 707-300C (and possibly the other variants as well) is truly uncontrollable in the lateral axis, or almost so, with flaps and spoilers deployed and the yaw damper inoperative, it is somewhat difficult to see how the aircraft could ever be safely flown without a functional yaw damper; takeoff and cruise wouldn’t pose too much of a problem, but landing, as a rule, involves a considerable amount of flap due to the resultant decrease in landing speeds, with spoiler extension being used to slow the aircraft down during the descent, and, if the yaw damper is indeed necessary for the 707(-300C) to be controllable with flaps and spoilers extended, one would expect a loss of control at some point during the descent/approach/landing sequence if it were flown without an operative yaw damper.
Why is the 707 so difficult to control with the yaw damper inoperative and flaps and spoilers extended?
1: The 707-300C was the most-produced civilian 707 variant; the other variants (-100, -100B, -200, -300, -300B, and -400), which differed mainly in fuselage length and engine selection, presumably behave similarly to the 707-300C for the purposes of this question.
2: A Boeing 707-300C built for Pan Am (Boeing customer code *21).
3: I am aware of only one case where Dutch roll actually caused an accident (and the aircraft still would not have crashed were it not for a generous heaping of pilot error). This was a 707-200 training flight in 1959, conducted with the yaw damper off, where the aircraft’s motions were greatly amplified by improper and excessive flight-control inputs by the pilots, causing a loss of control; the aircraft was eventually recovered from an inverted dive, but three of the four engines were torn off at some point in the process, and the aircraft crashed short of an intended emergency-landing site when flight-control damage from the resulting fire forced the remaining engine to be throttled down in order to maintain control.
4: Flap deployment increases the induced drag of the wings directly; however, this should not, on its own, cause a large increase in adverse-yaw tendency, as the flaps are located on the inboard portions of the wings (there being more room for them and their associated paraphernalia in the wide, thick wing roots than nearer the thin, narrow tips, and there being less additional wing-bending moment if the increased lift from the flaps is added as close to the fuselage as possible), while the ailerons (the increased induced drag from the downward deflection of which is the cause of adverse yaw) are located on the outer, unflapped portions of the wings, as far from the aircraft’s centerline as possible, in order to achieve the maximum possible roll control authority.5 Spoiler deployment increases the wings’ induced drag indirectly, by forcing the aircraft as a whole - including the ailerons - to fly at a higher angle of attack in order to maintain flight, causing an increase in adverse yaw.
5: Indeed, flap deployment could (depending on the aircraft and the exact flight conditions) even help in this regard, as the increased lift from the deployed flaps allows the aircraft as a whole to fly at a lower angle of attack, reducing the aircraft’s adverse-yaw tendency; the 737, a later Boeing aircraft, shows an example of this.