What were Presidents Nixon, Ford, and Carter's failures in domestic issues?
No leader ever achieves all their goals, particularly not in a democratic society where those goals can be countermanded by opposing parties. I wouldn't say that Nixon, Ford, or Carter were all especially successful or especially unsuccessful in terms of domestic policy; they had some successes and some failures.
Nixon's most significant failures in domestic policy mainly involved the Supreme Court; he appointed Warren Burger to the Supreme Court, hoping Burger would support his conservative views on various issues---but the Court voted against Nixon's views several times, including school busing, wiretaps, capital punishment, and abortion. The Supreme Court actually was quite liberal during the 1970s (in particular, this is when Roe v. Wade was passed), much to Nixon's chagrin.
Then of course Nixon's corruption was exposed, and he was impeached, to be replaced by Ford.
Ford and Carter both mainly failed in economic policy, though they were both elected during very hard economic times. OPEC had successfully hiked the price of oil around the world, triggering inflation and economic stagnation in all oil importing countries, which the US most certainly was.
Ford opposed using price controls to combat inflation (which many economists agreed with and still would today), but had no other effective means of fighting the inflation. He lost the election to Carter in large part based on poor economic fundamentals.
Carter focused less on inflation and more on unemployment, implementing a fiscal stimulus policy that saved many jobs but also triggered even worse inflation. He invested in renewable energy to reduce dependence on oil in the future. High interest rates ultimately quelled the inflation and the stimulus plan did actually restore employment, but not until Carter had already been replaced by Reagan. Reagan then essentially took credit for the economic recovery that Carter had created.