DMA, since 'Irangate' never actually happened, you'll need another reason for Carter to win the election. With this you have Iran appearing to side with Jimmy Carter for any of several reasons the American people will NOT like.
Humans rights take a major hit as Carter continues his trend of beating up on allies while ignoring more serious violations in enemies. To a large portion of American/Western opinion, 'human-rights' becomes slang for attacking non-leftist regimes, democratic or otherwise.
Democracy continues to die in the world.
Most Central American nations go into authoritarian regimes in response to Soviet-sponsored meddling in their internal affairs, starting with El Salvador and Honduras. Possibly Nicaragua actually invades Honduras and the US responds by conquering Nicaragua in 1985.
The collapse of democracies in South America under Carter also continues.
Japan, other allies of the US begin military build-ups in response to perceived American weakness. Possible nuclearization in Japan or Taiwan.
British loss of Falklands war causes 'hard-left' Labor government in UK, US bases closed. US quits NATO in 1985 unless...(see USSR below).
Carter attempts to carry out secret arrangements with Arabs during second term. Israel reoccupies Sinai, Camp David falls apart. Relations between US and Israel improve dramatically when GOP Dole(?) blames Arab leaders/Carter for dishonest dealing, Congress canceled all Egyptian aid anyway in 1982.
Soviet atrocities bordering on genocide in Afghanistan go unchecked. In the 1990s, following Soviet pull-out the Afghan mujahedin become prominent in terrorism; when asked about perceived lack of compassion for civilians they ask where compassion for the Afghan people was during ten years in hell.
Soviet collapse either takes place on schedule, or Soviets launch WWIII in attempt to force US and Western Europe to subsidize the Soviet economy. Either way, the world in the next 20 years is a poorer place in many ways.
Ask the then-Soviet Foreign Minister, Eduard Sheverdnadze, what might have happened if the Soviets saw ANY alternative to what they KNEW would be a time of agony for them, at best.
Carter's dishonest means of arranging environmental laws leads to a national backlash that erases most/all of his achievements, or worse. Possibly this includes a more energy self-sufficient US as nuclear power plants are built in the 1980s.
By 1984 Carter's second term he is a joke in most of the world and a disgrace in the US. Unable to pass any treaties, even with a Democratic majority in the Senate, the world's leaders become aware that Carter will deliver nothing and working with him may make enemies in the US.
Domestically the Democratic Party is in chaos as many are driven from office and more move to the right in self-defense. In effect, the US will have three major parties by @1988, a Carter Party, a South/Midwest Party, and the GOP which is the only national party. As the South/Midwest Dems begin to work with the GOP a super-majority forms, ironically leaving the GOP with far less need for the religious right.
***Alternative: Carter and allies keep control, the realignment under Reagan includes a higher percentage of the Catholics and union members, also a third or more of the Jewish vote.
Intense struggle within Democratic Party in 1990s between Carter/McGovern core and Clinton/Gore moderates. Possible split of party, 2-4 elections with no legitimate alternative to GOP.
Bloody carnage in Iran-Iraq War continues, no doubt mujahedin also comment on utter lack of Western concern for 2 million+ death toll. Ends in late 1980s when Iranian attempts to block oil tankers leads to US reprisals and Iran sues for peace. Much talk about how the US was 'on Iraq's side' all along later.