What were the shortcomings of literary digest’s 1936 presidential poll? how does modern polling correct these problems?

There were two main shortcomings with the Literary Digest's 1936 presidential poll:

Sample bias: the magazine selected 10 million people out of three sources: telephone directories, club memberships, and magazine-suscriber lists. These sources gave the sample and middle an upper middle cass bias because in the epoch, few poor people owned telephones, were members of private clubs, or were suscribers of magazines. Nonresponse bias: Literary Digest wanted to survey 10 million people, but out of the 10 million people who received the poll, only 2.5 million people responded. This is called a nonresponse bias because the people who respond surveys have specific qualities different from the people who do not respond surveys.

Modern-pollsters tries to be more careful when selecting a sample: it should be representative of the population as a whole. Pollsters also have to deal with nonresponse bias, therefore, they try to send their surveys to people who are more likely to respond.