What were the challenges for making a refrigerator?

The largest challenge was (and still is) finding and making refrigerants that are both safe and effective. The earliest refrigerants were either highly toxic and/or highly flammable, many people died because of refrigerators using these refrigerants. With DuPont's invention of freons which are both nontoxic and nonflammable and thus seen as the ideal refrigerants, the refrigeration industry took off. But with the discovery that freons destroy the protective ozone layer of the atmosphere it has again become necessary to seek new refrigerants, most of the current options are slightly flammable!

Another challenge was to develop seals for the pumps that compress the refrigerant that won't fail prematurely, allowing possibly toxic or flammable refrigerants to escape. Albert Einstein invented an electromagnetic pump with no moving parts (thus needing no seals), but the invention of "safe" freons made this unnecessary (however it later found use in liquid metal cooled nuclear reactor designs).