Propping up a military dictator didn't work out for us whatsoever. We earned the hatred of the Iranian citizens and had to deal with the hostage situation. There are always unintended consequences for what we do around the world.
There's no evidence that Iran has a nuclear weapons program, only the same kind of propaganda that we heard prior to the Iraq war. And no, it's not worth the price in blood and treasure, especially considering we don't know what else could go wrong on top of that.
Propping up the Shah, if that's what we did, did work out for us; not propping him up in 1979 is what got us in trouble.
There's lots of evidence that Iran has a nuclear weapons program, but it's not an airtight case, if that's what you mean, however, is that because there is no nuclear weapons program or because Iran refuses the IAEA the full access to its nuclear programs it is asking for? There are only three reasons I can think why Iran would continue to deny the IAEA the full access it seeks: there is a nuclear weapons program, the regime wants the world to think there is because it makes Iran look tougher, stronger and more dangerous or the leadership is either stupid or crazy.
It's true that we don't know what might go wrong if we do intervene, but we also don't know what might go wrong if we don't intervene. If we had known in 1979 what not intervening to keep the Shah in power would lead to, would we have acted differently? After all, Saddam would not have attacked Iran if Iran still had the support of the US, and millions of lives could have been saved if we had intervened to keep the Shah in power. Arguably, Saddam would not have invaded Kuwait if not for his failure to make any gains from the years of war with Iran, and had he not invaded Kuwait, we would not have become involved in the first Gulf War, and we would not have had to increase our presence in the ME, especially in Saudi Arabia, to contain Saddam afterwards and one could argue that it was the increased US military presence in Saudi Arabia to contain Saddam that fueled the growth of al Qaeda and that led to 9/11 and our present wars in Iraq, Afghanistan and, to some extent, Pakistan.
So, on balance, what could have gone wrong if we had intervened to keep the Shah in power in 1979?