Spying might be worthwhile for countries with money-increasing sliders and ministers.
Naval espionage is a cheap mission with good success chance that may be useful for Germany, as it displays all convoy routes of the targetted country on the supply map for a short while.
I find that as post-Bitter Peace Germany, I have more IC than I need for production, etc., so that would also be a good time to invest in espionage just to exploit the available resources. ... Of course at that point the typical game is also de facto won, so that usefulness is relativised somewhat.
Spending a token amount on espionage and investing exclusively into counter espionage seems to be a good idea to prevent the AI, which will spy no matter what, from raising dissent, delaying production or stealing blueprints, etc. I usually invest one to three clicks on the slider for that purpose as any country.