Specialists
When creating specialists look carefully at the growth bar figure, look at the jumps up/down in growth each time you add one. The long term effects of using specialists is very important to balance right, so as not to choke growth, but not use too little for science.
You can specialize your whole empire using specialists in every city, but choosing the right time is the skill.

Entertainers:
Good if you have a small amount of cities low in happiness but martial law is preferable. Using them in small size cities is bad for growth. A city with 72 happiness can go without revolting sometimes but its only a matter of time, so you should still aim for at least 73 happiness.
Farmers: You can use farmers in small or low growth cities. 1 farmer in a size 1 city until the city grows to size 2 or 3, then the city becomes more self-sustaining. Cities near mountains benefit from farmers to keep their growth moving, but be careful not to use too many or you take away too much production and commerce from your empire.
Laborers: Can be used in any large city, especially in the final stages of a war to produce more units.
Merchants: I have yet to find a good use for merchants...

Scientists:
Use in any large cities with good growth. Don't use scientists in cities with lots of mines, this will reduce the production and mean you spent Public Works building mines for nothing.
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