The answer to this question depends on what the OP means by "mass." Counter-intuitively, mass defections of a large group at once was a feature that typified GDR defections after the Wall came up. The Berlin Wall was the final leg of a process by the SED dictatorship to clamp down on Republikflucht (flight to the FRG). The GDR had already made fleeing the state illegal in the 1950s and this criminalization led to larger groups leaving the GDR lest they be punished by the state if they remained in the country. Escaping the Wall, or even going through the labyrinthine legal process for emigration often hinged on getting everyone out. That said, West Berlin was one of the epicenters for the pre-Wall Republikflucht and this was a mass phenomenon. Refugees might come in groups of one or two, but collectively they represented a mass movement of Germans from East to West.
One of the major reasons West Berlin was a major center for Republikflucht was that it was the safest alternative for a successful escape. The inner-German border was crossable in places through the 1950s, but it was increasingly becoming a military border. The GDR and the Soviets had already expelled some residents of the border for military reasons and the area was heavily patrolled and armed as the Cold War escalated. Barbed wire, tank traps, and land mines became common features of the inner border starting in the 1950s. Navigating this area required a degree of local knowledge, timing (border troops sometimes deactivated the mines in winter lest snow trip them), and luck. The Wall's erection actually accelerated the process of arming and fortifying the inner German border. This somewhat staid and propagandistic US Army educational video from the 1970s illustrates how the border was militarized and quite formidable.
West Berlin in contrast was a much safer area to make a dash for the FRG. The city was large and had a large number of entry points for a would-be Republikflüchtige. Wartime agreements meant that the East ran the city's overground S-Bahn rail routes. A good many defectors simply bought a ticket and left at one of the West Berlin station stops. The SED tried to staunch this method of escape, with MfS informers at rail stations and ticket booths, but it was too large of an area to effectively police. The Berlin's Mitte district fell under the Eastern zone, but it also had underground U-Bahn stations, which the Western zone ran in typical wartime agreement fashion. Other refugees simply walked across the border checkpoints from East to West Berlin. While such crossings were not without risks, there was considerable East-West foot traffic prior to the Wall. There were a not insignificant number of migrant workers who worked in the Western zone while residing in the GDR. A number of refugees could bluff their way past border checkpoints claiming to visit family members or going on a brief holiday. Although crossing the border with intent to flee became illegal in the 1950s for GDR citizens, it was very difficult for the SED to staunch this outflow of people via West Berlin. A 1961 report by the MfS concluded that for every one individual stopped by border and police controls, some six evaded these controls. West Berlin had become after 1953 the dominant egress point for a prospective Republikflucht; this graph (and it is a little pixelated) from the Federal Ministry of Refugees shows how Berlin, the red-shaded line, played an outsized role in the refugee crisis.
It was not just the numbers of refugees that was so damaging to the GDR but the fact that many of them were young and relatively well-educated. The West German economic miracle coupled with the sputtering the GDR's planned economy meant there was an attractive incentive for these individuals to make the flight to the West. FRG business firms played a role in recruiting such skilled laborers as their native talent pool dried up in light of the Wirtschaftswunder. Other economic incentives for GDR professionals and skilled laborers to leave the state were the stringently controlled and often corrupt planned economy which limited promotions and sometimes placed SED loyalists in senior management positions. The GDR's reliance upon shock labor action to meet quotas, common in the Eastern bloc economies, made the Western model more attractive for a number of laborers who swallowed the dream of working less and earning more. A not insignificant number of these laborers were disappointed that the bounty of the FRG's economy was not as open as the image of the West promised. These returnees were always outnumbered by those who remained in the FRG and a good many returnees themselves re-fled the GDR as the SED often subjected them to legal discrimination for mounting a Republikflucht in the first place. Other refugees fled because of fears that the GDR would reintroduce conscription or to escape the collectivization of agriculture. Political repression was also a factor as the SED was hardly a popular dictatorship and the 1953 Berlin revolt did demonstrate that the state was more than willing to use tanks and military force to suppress its population. Fleeing to the West also was tied to people's estimation of the Cold War tensions. The colder the Cold War got, the more some GDR citizens thought it was best to take advantage of the Berlin option while it was still available.
The net result of the mass epidemic of Republikflucht was that it became something of an existential crisis for the GDR. It a propaganda failure and an embarrassment for the GDR. This American newsreel from 1958 was typical in how the West did present the crisis to its own population and the world. More seriously, the outflow of skilled workers damaged the GDR economy at a moment when it was precariously recovering to prewar levels. While the push-pull factors for flight were present in other Eastern bloc countries, the division of Germany was a perfect storm that created the refugee crisis. There simply was no alternative of a West Hungary or Federal Republic of Poland for those dissatisfied with Communist rule. While such refugees certainly did exist during the Cold War, they often had to start life from scratch in what was essentially a foreign country. The FRG held that all ethnic Germans could apply for citizenship in the Republic. Bonn's position was that it was the sole provisional government for Germany prior to a final peace treaty and the GDR. This lowered the threshold for refugees as there was a guaranteed legal status should they make the leap to the West. The common culture and language as well as familial connections likewise made it less of a risk to flee. These same factors likewise opened the FRG up to greater penetration by the MfS and other spy agencies of the Eastern bloc, but this was a small consolation given that these same factors led to a hemorrhaging of some 3.5 million Germans between 1945 and 1961.
Sources
Harrison, Hope M. Driving the Soviets Up the Wall Soviet-East German Relations, 1953-1961. Princeton: Princeton University Press, 2011.
Large, David Clay. Berlin. New York: Basic Books, 2007.
Major, Patrick. Behind the Berlin Wall: East Germany and the Frontiers of Power. Oxford: Oxford University Press, 2011.
Ross, Corey. The East German Dictatorship: Problems and Perspectives in the Interpretation of the GDR. London: Arnold, 2010.
