Given that political tensions in Iran had been escalating many years before 1979, it's likely that the Iranian Revolution would have taken place no matter who won in 1976. However, had Carter been elected, Iran probably would have had an Islamist rather than a Communist revolution. The reason is that Carter's plans to make promoting democracy and human rights the centerpiece of America's foreign policy meant that he would have been far less willing to lend the Shah the same kind of unconditional support that Ford lent. Without this kind of support, it's highly unlikely that the CIA would have assassinated the Islamist's most prominent leader, Ayatollah Khomeini (nor would Savak have been emboldened into assassinating Ayatollah Montazeri, who was Khomeini's designated successor).
As we all know, these assassinations allowed for the left-wing cleric, Mahmoud Talghani, to become the revolution's de facto leader and to later go on to form the Islamic People's Republic of Iran. However, had neither of these assassinations taken place, Ayatollah Khomeini probably would turned Iran into a repressive Islamic Theocracy rather than a republic based upon a fusion of Islamic and Marxist principles. Had Iran become an Islamic theocracy, it's likely that Islamism would have become a major political force in the Middle-East rather than a marginalized ideology. Perhaps this could have prevented Bachir Gemayel from fully consolidating his hold on power in Lebanon in 1982?
Another interesting case to consider would be Afghanistan. Without Talghani's advice, guidance, and support, it's likely that tensions in Afghanistan between Islamists and Communists would have continued to escalate. An Iran under Khomeini probably would have lent full support to the various Islamist factions in the late-70s and early-80s, which likely would have destabilized Afghanistan. I know I'm going out on a limb here, but I'm willing to bet that the Soviets would have responded to this by invading Iran and Afghanistan because Iran clearly would have presented itself as a threat to the Soviet's hold on Central Asia. However, Iran and Afghanistan's terrains would have been ideal for guerrilla warfare, so this likely would have turned into the Soviet's Vietnam. Going out on another limb, I'm willing to bet that had this war gone on long enough, it would have incited an Islamist rebellion in Central Asia that in turn would have sparked a civil war in the Soviet Union along ethnic lines sometime around the mid-to-late 80s.
As for domestic matters, assuming that Reagan is elected President in 1980, America would have likely been in a much weaker position than it is today. For one thing, Reagan would never have implemented President Udall's "Green-Green Solution," which revitalized America's economy and made us far less dependent on oil for energy by heavily investing in high-speed rail, public transportation, renewable energy, and the manufacturing of electric cars. Given how unstable the Middle-East would have been in this scenario, America would likely have suffered from reoccurring energy shortages and/or gotten bogged down in frequent military ventures in the Middle-East in order to stabilize the region and secure its oil interests. Since Reagan would not have taken on big oil in the same way Udall did (which, as we all know, led to Congress passing legislation in 1987 that created a system of public finance for all election campaigns), the latter would have been a very likely outcome in TTL.