what sort of obstacles did the Einsatzgruppen have while commiting this mass murder?
In his book titled Masters of Death, which describes how special German SS troops in World War II committed mass murders, Richard Rhodes writes that some of the men found the killings difficult in various ways, both practically and morally.
For example, when victims were shot at the edges of mass graves, their bodies would often fall into the graves in disorganized ways, thus wasting space and necessitating the digging of more numerous and narrower graves. This “problem” was solved by making potential victims lie in the mass graves immediately next to one another, like sardines in a can, so that they could be shot and killed in ways that wasted the least space. This method of killing was actually called “Sardinenpackung -- sardine-packing.” As if this were not bad enough, Rhodes reports that
The Jews had to lie layer upon layer in an open grave and were then killed with neck shots from machine pistols, pistols and rifles. That meant they had to lie face down on those previously shot.
Another such “problem” involved how to efficiently kill mothers and the young children they were often holding. According to a New York Times review of Rhodes’ book (cited below), one solution
was devised at a killing site in Latvia: mothers with infants had to hold their babies over their heads; one man shot the mother, one the child.
However, because such personalized killing was often morally difficult even for hardened SS troops, more impersonal, anonymous means were invented, including the gassing of large groups of people. After all, the people being gassed were usually invisible to the people in charge of gassing them. Indeed, it was usually other Jews who were forced to remove the gassed bodies from the chambers so that German soldiers would not have to touch their bodies.
Rhodes’ book reports that even Heinrich Himmler, head of the SS, was squeamish about watching the killings of individuals and worried that participating in such killings might take a psychological toll on his elite troops. With the invention of killing by mass asphyxiation, the so-called “final solution” became even more “efficient” than it had been already.