OVERPOPULATION
One point above all, according to me overpopulation is never a problem but an advantage. It gives you manpower, shields and money. Just manage their mood giving them luxuries.
I usually play 3.6.1 (cash, research, luxuries). A t lower levels of difficulties it is enough to prevent revolts and reduce entertainers.
Also build temples, cathedrals and colosseums to help this.
Happy people need less specialists (entertainers) and less specialists (until city is size 21) means more people to work and produce especially food. Unhappy towns need many entertainers and may go into starvation.
CORRUPTION
Someone here wrote an interesting article on how to prevent corruption. It is interesting even if not always applicable.
It says to create an elliptic empire with the capitals and the forbidden palace at the two centers.
This is ok (if the opponents will let you), in huge pangea maps, non always in continents and never in archipelago maps.
I'd say, instead, to build cities as fast as you can in the beginning, NOT building the forbidden palace until you control a large area of growing towns far away the capital. Then build the forbidden palace in the biggest town, possibly in the middle, but surely in the one with the fastest production (it can't be rushed).
Courthouse normally save 1 to 3 shields, not more, police stations are more effective but they are expensive and long to build without a factory, and they also become available too late for me.
Huge maps can be won in diplomacy by the year 1500, more or less, at lower levels of difficulties and so police stations come too late.
Hope to have been helpful.
GL
