I can't answer for mass hysteria, but there has certainly been some false calls which provoked an often vigorous response:
The 1995 Norwegian rocket incident, where a Black Brant sounding rocket from the Andoya Test Range was mistaken as a threat by Russian missile warning radar operators, as its particular trajectory apparently mimicked that expected by either a Minuteman missile flying over the pole or that of a Trident missile fired from northern waters. A single missile is generally not to be expected in such attacks, but their was some belief that a single missile detonated at high altitude could be used to as an EMP weapon to knock out over-the-horizon and ABM radars as a precursor to a full on strike on Russia and Moscow. Alternately, there was also concern in Russian analyst circles that the Trident D5 missile had the CEP (circular error probability, ie the accuracy) and defence penetration capability to be a viable weapon for use in a first strike scenario to decapitate Russian leadership if fired on a low level "cannonball" trajectory where it could avoid detection by ABM defences and afford little reaction time to Moscow. This incident was apparently serious enough to cause the Russian "nuclear football" to be opened and prepped, and contact to be made with land and sea based rocket forces. However, as the sounding rocket continued its flight it was realised not to be a threat and defenses were stood down.
During the Cuban Missile Crisis in 1962, Volk airbase in Wisconsin was used as a dispersal point for B-47 bombers. On 25 October 1962 a guard at the Duluth Sector Direction Center noticed a figure climbing the perimeter fence and sounded the alarm linked to all surrounding airbases, believing that saboteurs where attempting to attack the aircraft on station. Due to faulty wiring this actually triggered an alarm scrambling F-106A nuclear-armed interceptors. Security guards responding to the intruder quickly found out that it was actually a black bear, and were able to halt the F-106's before they got airborne.
In 1979, a false attack warning was interpreted by operators at North American Aerospace Defense Command (NORAD), when a tape containing an attack simulation exercise was accidentally left in an early warning computer system. It was regarded seriously enough to cause several interceptors to be launched as well as the National Emergency Airborne Command Post, although without either the president or the secretary of defence which it was meant to carry. NORAD was able to disprove and cancel this threat warning within 6 minutes by cross-referencing with both PAVE PAWS early warning radar and warning satellites which showed no launches had taken place. This was one of several incidents of the same era caused by software issues: A similar incident occurred in 1980 when a faulty computer chip gave erroneous readings of land-based and submarine missile launches. The response to this incident was less vigorous as operators noted that every warning listed the amount of missiles launched, and all the totals had zeroes within the number replaced by twos (where the computer display normally listed number of launches as 0000, they were instead coming up as 0002, or 0202 etc), thus the operators realized the numbers were not rational.