I honestly don't know how to menage efficiently with shield waste problem, it has a huge negative impact (at least 10 cities with 1 shield only) on production. Moreover, civilopedia is silent about this topic.
Yes, if you had to choose only one thing about Civ3 that
really annoys even the most enthusiastic players, it's the corruption issue. This is partly hardcoded, part moddable in the .biq (using the Civ3 Editor), but can only be dealt with in a few limited ways in the standard epic-game.
First and foremost, you need to switch to a lower-corruption government ASAP after you begin a new game. You start in Despotism, which has the highest-but-still-functional corruption level of the 8 default 'govs' (only Anarchy's corruption is worse, but then you can't build
anything), but if you 'beeline' to Republic (or Monarchy) in the Ancient Age, you can reach it in 5 techs or less -- depending on what you start with, what you unlock from goody-huts or trading, and/or whether you can reach Philosophy before any other Civ (if you do, you can choose 1 additional tech for free).
Although Democracy's corruption level is somewhat lower than Republic, it doesn't get unlocked until a
lot later in the game, and you don't want to stay Despotic that long. If your Civ is Religious (Anarchy between govs is limited to 2 turns), you
may want to consider switching govs a second time in the late game, to Communism (you no longer have a low-corruption core and high-corruption peripheries: instead, your total wastage gets shared out relatively evenly among all your cities). Under Communism, it becomes possible to hand-build stuff everywhere -- but at the cost of all your highly developed core-towns each becoming much more mediocre producers -- so switching to it is very situational.
To deal with corruption in your 'core' towns (those nearest your Palace), you can build Courthouses (needs Code of Laws) and later Police Stations (needs Communism). In more marginal towns, you can also assign citizens as Policemen (decorrupts 1 shield and one gold per policeman; needs Nationalism) and/or Civil Engineers (produces 2 uncorrupted shields for
buildings only; needs Replaceable Parts).
Under non-Communist govs, though, it's not really worth doing any of those things in the >90% corrupt boondocks: just pack the towns in those areas as tightly together as possible (="Infinite City Sprawl", or 'ICS'), fully irrigate (and rail) the surrounding tiles, and use these areas to build Workers, Settlers and/or Wealth, while their excess citizenry (supported by the excess food supply) work as Taxmen (gives 2 gold per head), or Scientists (gives 3 beakers per head). This tactic is known as 'gold/beaker-farming'.