I usually put it at 10% - 20% (10% most commonly) after discovering Alphabet and before discovering Code of Laws and building a few Courthouses.
I am addicted to the Great Wall wonder, and the extra boost to espionage from the 10-20%, plus great spies, lets me stay at least even on research.
I think the slider is most useful at the beginning of the game, soon after Alphabet is researched, but before Code of Laws.
It is handy sometimes when at war, and I will tend to give espionage a boost at some other moments in the game, generally if I am in a war (or a cold war) with an opponent. By "cold war", I mean a spy war, not necessarily a nuke-building war.
Finally, in the end-game, if someone else is going for space race, I will pump up my espionage and send spies to their cities to sabatoge production. If I can see their cities' production, I go for sabatoging Apollo, since that hurts the most. If I can't see their production before they enter the space race, I really crank things up against them, set the slider to 10-20%, and target heavily.
Sam