The Iranian Occupation was one of the biggest mistakes Britain ever made.
From what a buddy of mine who was in the government, it turns out the occupation occurred because the US refused to help the UK plan a coup to Mosaddegh, even with fears of communist ties.
Instead, it was when conservatism as we knew it kinda died. When word of this came out and so on, the Democrats used to pretty much slaughter the Republicans in the elections, especially those that vouched for invading Iran. This is what managed to get the Second Bill of Rights passed (if a toned down one) by them. This also caused a schism between pretty much Europe and the US, with the latter's distrust to the former due to colonial matters and then the former accusing the US of hypocrisy due to the US's not nice practices toward Latin America.
Granted, the Cold War ended and the world was in a more fractured state as Russian and Chinese opportunism instead led to the nasty schism between them and let's face it, Mao and Stalin didn't die natural deaths as we were led to believe (well, maybe Stalin given his increased alcoholism.) China did cool down significantly toward the US and definitely reorganized itself once the Cult of Mao dissolved. Heck, it's why the US trusted China to help rebuild India after the rebellions and now one of the US's closest allies.
The Labour Party has been working to fix Britain's reputation when they finally won back in the 70s and been doing a pretty good job. Iran is barely talking to them (outside of each other's leftish groups and the younger generations) however.
Without the occupation, none of this would've happened. China and Russia probably still would've split, but the crack in relations and alliances wouldnt have caused the Cold War to collapse into a tension-filled era. Granted, the USA technically won (least in terms of spheres of influence since all of the Middle East but Turkey and I guess Egypt is with them, the latter having stayed with Britain after the US backed Israel in that war.)
With Britian out of the way, the US basically went over to manage the Miiddle East for a bit. Or basically give Iran Afghanistan along with Baluchistan and part of what was Iraq (the Shia dominated part) along with making Kurdistan its own nation and the rest of the land along with what was Lebandon and Syria to Jordan. This did mean we got the Hashemite-Saud War, but once the Hashemites patched things with Israel, Saudi Arabia got crushed and now we have The Hashemite Kingdom of Arabia controlling most of the Peninsula (barring Yemen, which has been growing more Jewish by the year and pretty much Israel's wife) and Oman (who just wants to be left alone.)
Granted, this did mean Europe would stick closer together and they eventually managed to start fixing things up with their former African colonies. Without Britain's screw-up, they would've botched it.
Russia's attempt at trying to influence the EU has been somewhat hilarious to say the least, but they did legitimately change for the better. If nothing else, Russia is now a pretty all right place though they're trying very hard to continue Russian culture before the USSR and the Mafiya is still a problem for them.