I think the thing that I would like to see most is having the corruption index tied to the player and not simply an arbitrary setting. What I was thinking of is making it dependent on the human players willingness to micromanage his cities. The closer the human player keeps track of what his city governors are doing, the less corruption in the city.
The way I envision this being done is having the computer keep track of how many turns occur between the human player checking on city progress. If checked between 1 to 5 turns, corruption is absent. If checked between 6 and 10 turns, corruption is minimal. If checked between 11 and 15 turns, corruption is problematic. If checked between 16 and 20 turns, corruption is rampant. If the player has not checked the city in 21 turns, corruption is catastrophic, and effective city production is no shields, no commerce, and no beakers. The Ai corruption would reflect the human players level, although modified based on the game difficulty setting. Say, at chieftain level, the AI would not improve past problematic, while at Sid level, the AI would not suffer any corruption at all. Corruption in communism would stay at communal, as it appears to be endemic with that type of government.
The greater the number of cities that a player has, the lower the likelihood that a player will keep close tabs one any given city, and the higher the level of corruption. This would include the "science farms", with the longer the player ignores the city, the fewer scientists there are and the more taxmen and entertainers there are.
The choice of government would influence mainly worker productivity and happiness levels, with democracies, republics, and monarchies happier than despotisms, feudalism, and fascism. In fascism, the threat of the secret police should produce citizen unhappiness, while fascist Japan (i.e. pre-WW2 Japan) was remarkably inefficient in its production, manpower utilization, and military standardization.
I would hesitate to say the democracies are less corrupt that despotism, based on my observations of living most of my life in the less-than-great state of Illinois, and in close proximity to Chicago without having lived in Chicago per se. Chicago could be most accurately characterized as a democratically elected despotism, with Illinois in general being a democratically elected feudalism, with legislative seats and governmental offices being passed down from parent to child on a regular basis.
My other observation, based on having served as a local government official on a body having taxing powers, is that the level of corruption increases with the increase in the level of government, although some governmental types, such as despotism, increase faster than others. Many of the South American governments are democratically elected, but are also notorious for corruption, and I will not even begin to comment on most of Africa and some of Asia. In line with this, you could make some civilizations to have a higher tendency for corruption than others, and also have some adjustments to corruption level based on the number of cities possessed. The greater the number of cities, the greater the chance for significant corruption, unless the player exercises close micromanagement.
Basically, the idea is to shift the responsibility for corruption from the game to the human player.