One potentially very significant effect of the Pahlavi regime continuing would be the impact on the Iraqi nuclear weapons program.
Without the Iran-Iraq war, Operation SCORCH SWORD wouldn't take place in 1980; this might or might not have delayed the Osiraq reactor becoming operational. Or rather, Israeli intervention - the Israeli government apparently having been planning an air raid on the reactor since 1979.
In OTL, Operation OPERA had significant Iranian support, including aerial reconnaissance, a preparatory air raid on the H-3 air base, and arrangements for Israeli aircraft to divert to Tabriz Air Base in an emergency. The extent to which Iran would support such an operation in the alternate timeline is open to question: on the one hand, it's very unlikely that Iraq would be at war with Iran; on the other hand, Israel would likely have better relations with the Shah's government than with the Islamic Republic
If the strike does not go ahead, it is possible that Iraq's nuclear weapons program is accelerated. Even if you accept the argument that Osiraq itself had no military role, the knowledge and experience gained would have benefited Iraqi nuclear scientists, and Iraq may have felt that it didn't need to conceal the program as comprehensively.
Alternatively, the absence of the attack might mean that Saddam Hussein does not feel the need to develop the ability to deter Israel. In that scenario, and especially without an Iran-Iraq war, the Iraqi conventional and WMD build-up of the 1980s is greatly reduced, although likely not entirely: the Iranian buildup would demand some kind of response. In either case, if the attack doesn't happen, the international backlash against Israel never happens, and UNSC Resolution 487 is never passed.
If Operation OPERA does go ahead, on the other hand, it's likely to use A-4s instead of F-16s - the aircraft used historically were originally ordered by Iran and diverted to Israel after the revolution. Without a revolution, Israel wouldn't have got F-16s as quickly. This is likely to impact on the capability of the strike force, though I'm not sure exactly how. The result might be greater likelihood of losses, or reduced likelihood of destroying the target. Without the war against Iran, Iraqi defences would likely be less alert, but also wouldn't be as focussed towards the east; this could go either way. But, Iraq would also likely feel more willing to retaliate against Israel in this scenario.
In any of these cases, the subsequent impact on regional politics is potentially immense. And, with no Iran-Iraq war, it's probable that there's no subsequent Iraqi invasion of Kuwait. In turn, that means no massive American troop presence in Saudi Arabia to deter Iraq, and less anti-American sentiment in al-Qaeda and the wider Islamic world. Which, in turn, means that the entire post-1991 geopolitical environment is different.
There would of course be impacts on equipment sales and on the defence industrial base in various countries, but they're far less interesting than the geopolitical and grand strategic changes. And I haven't even touched on the possible impact of Iran developing an economy comparable with many European countries, which was possible if reforms had been better implemented. There's plenty of blame to go around there, of course.