The legally elected PM (a Dr. Massadegh - TIME's Man of the Year in '51) broke the back of the UK's sweetheart oil deal. The UK sued in the Hague and lost. Within two years MI6 and the CIA orchestrated the coup and put Reza in charge. That lasted only two days before the people of Iran chased him out. The CIA used the Army to put him back in. After thirty years of the Shah (and SAVAK) the people of Iran threw him out again.
Certain folks here like to paint the Reza years as a progressive utopia and place the blame for the revolution squarely on US shoulders. I've yet to read of any revolution, in any country, at any time in history that was executed by a populace that was content, respected, safe and hopeful.
The folks who want to bring the Reza "dynasty" back to power remind me of the elements in the Bay of Pigs who were holdovers from Batista's regime. Iran threw the shah out, I don't want to see one drop of US blood spilt to put his son back in his palace.
If Iran has had enough they will make a change, they've done it before.
It's worse than that. The joke in this is the presumption of all ruling dynasties.
The shah is just the successor of the original pahlavi shah, Reza Khan, who was a military officer and minister of war under the last ghajar king, but who led a coup and crowned himself shah. The ghajar dynasty usurped the throne from the zand dynasty, and so on and so forth.
Iran's recent history seems to be nothing more than a series of rulers being imposed and deposed by various outside powers (such as Russia, Britain, and the U.S.) and internal revolts. Add in ambitious religous nutballs, and you have a real mess.