You should stop play once you reach a point at which a decision must be made that has not yet been polled.
The military advisor will get general orders for units - explore this way, tip that hut.
The science advisor will keep a research target toward which you must research. If you catch up in the game, wait for new orders.
Rush buying should be approved by the minister of trade. (did our first president do this?
) As should caravan commodities and destination cities.
City workers will be optimized by our city planner. Now that he will have the save game, he can poll for maximizing shields, arrows, or food for particular cities.
City build orders must be taken as a general build order list. The city planner does that, too. E.g. defender, settler, temple, defender, or some such. Exceptions should be polled, such as a wonder or non-ordered improvement. Don't stop every time a city is done with something, you'd poll between every single turn - and the game would last forever.
It will always be the case of the president having final judgement. If 5 barbarians appear next to a city, by all means just change production to a unit, no need to poll. If a city or two have no build orders, use your judgement. If it is good, you might be re-elected...